There are so very many assumptions on a theological extrapolation like this that I think it is worthwhile to spend a moment discussing them. For instance, one of the most significant assumptions is revealed by Ollie Wallflower asking these questions from the perspective of the world which exists now. However, there is no inherent need for an 100% spiritual being (God) to create an entirely different kind of realm (physical) for His creations to live in; a realm where their interaction with spiritual beings is limited at best. The fact that we live in this physical world is, to a large degree, why these questions have any real significance.
Also tied into these questions are the assumptions of divine purpose, divine planning, and a divine defined timeline. It is easy to imagine a perfectly good God who has no explicit purpose for His creations, other than for His entertainment of sorts, objects for His affection and delight. It follows then that a perfectly good God has no inherent need of a multi-millinia plan, and no need of a timeline to say when the physical realm will come to an end, or be remade, or whatever your belief. To a lessor degree, these questions have significance based on the Christian presumptions of purpose, planning, and timeline.
So, let's acknowledge that we are working under the above noted, and probably many more, assumptions which are richly steeped in Christian theology, and move on from there.
The next hurdle is defining what is perfectly good, or omnibenevolent. “Good” has so many varied uses in our language that perhaps we would do better to define it as love in this case. What does a perfectly loving God look like? Well, because we are building this argument on Christian fundamentals, why not use a Christian definition of love? We'll look at one of my favorite, well written sections of verse, 1 Corinthians 13:4-7, below for reference:
"Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It does not dishonor others, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres." NIVChristian or secular, I think that's a good definition for love, period. So let's promote this as our concept of what an omnibenevolent, perfectly good, all-loving deity would be like. OK, now let's attack the questions:
Can an omnibenevolent God insist that He alone be acknowledged as God, or must He allow for the belief in other gods, or in atheism, as well?
Love is patient, ergo, God must be patient with people who believe in other gods or no gods.
Love is kind, ergo, together with patience, God should allow people to come to the truth about God on their own time.
Love does not envy, ergo, God has no cause to be jealous over people believing in other gods.
Love does not boast, ergo, God has no cause to insist that He alone be recognized as the only God.
Love is not proud, ergo, God has no cause to even bring up that He is the only God.
Love does not dishonor others, ergo, God has no justification to humiliate or punish those who do not believe in and accept Him.
Love is not self-seeking, ergo, God should not focus on His own displeasure in those who do not choose to follow Him.
Love is not easily angered, ergo, God should not be angered at humans with all of their varied circumstances, imperfect knowledge, and imperfect capacity for understanding that there are no gods but God.
Love keeps no records of wrongs, ergo, disbelief should not be an issue for God.
Love does not delight in evil, but rejoices in the truth, ergo, God should be simply happy when any human does come to accept the truth about Him.
Love always protects, ergo, God should protect even those who do not believe in and accept Him.
Love always trusts, ergo, God should trust that all people will come to believe in and accept Him.
Love always hopes, ergo, God should perpetually hope that all people will come to believe in and accept Him.
Love always perseveres, ergo, God should endure those who do not believe in and accept Him.
Can an omnibenevolent God allow evil--even if only for a time--and still be considered "good?"
The question only makes sense if God is assumed to be omnipotent, or at least powerful enough to prevent evil. It also draws into question what our assumptions are regarding evil. We know sin is an act which is against the will of God. Is evil the same as sin? I don't think so, at least not in our present-day vernacular. Evil appears to have a detrimental connotation, and is some subset of more-serious sins. We would not call someone who routinely breaks the speed limit “evil.” On the other hand, a serial killer is someone for whom the label “evil” seems appropriate. For lack of a better definition, evil involves acts which are in active, cognizant, and polar-opposition to love, and most often infringe upon the will of others.
Little in the 1 Corinthians 13:4-7 definition of love is specifically defiant of such evil acts.
Love is kind, ergo, God should act to prevent evil in kindness.
Love always protects, ergo, God should protect people from evil actions.
[EDIT NOTE: The NIV "always protects" is not the best translation. It should read "always endures all things" instead. However, given that no one would be considered "good" if they did nothing to prevent an evil act or bad act which was in their power to prevent, protect is a relevant definition for love.]
A typical Christian objection to this is that such an act of protection or preservation by God would impede on free will; that somehow absolutely free freewill is necessary to result in the purest love. However, this again is based on assumption. Our free will is impeded from the moment of birth by nature of this physical existence. For example, I desire to see the spiritual world, and I desire to fly like Superman, and I desire to teleport because air travel is just too slow. However, I can't choose to do any of those options, as they are simply not available to me. They are restricted from my freewill. Even beyond these super-powers, my freewill is restricted by circumstances. If I was a thief, and my desire was to have everything I ever could want, I could not achieve that because being just one person with a limited lifespan limits the fulfillment of my freewill. So our perception of what freewill is inherently accepts that our “natural” boundaries are the assumed acceptable limits of freewill.
That said, is it possible for God to allow people to have freewill but not allow evil? I think so. Have you ever seen an invisible fence? An invisible fence is a product is designed to keep your dog in your yard. You equip the dog with a special collar which, by radio frequency, activates an unpleasant shock to the dog when it tries to go beyond an established barrier (set by a buried wire). The only thing which activates the collar is crossing that threshold. In other words, the dog is completely free to roam on its own will, dig up the flower beds, chase squirrels, “water” the trees, etc. As long as the dog does all that in the yard, it receives no shock.
What if God equipped us all with a type of invisible fence to prevent evil? We could still do (nearly) anything we wanted to do on our own freewill. However, let's say that I had become angry at my neighbor because he had parked in my grass, and I decided I wanted to kill him because of that. The moment I grabbed my gun with the intent to slay him, God's invisible fence kicks in and I start to vomit. (God could easily do this if He is truly omniscient and omnipotent.) The nausea subsides, I grab the gun with the intent to kill my neighbor again, and immediately I start vomiting again. After a few cycles of this, I give up on the gun and decide to strangle him. As I start to walk over to his house with this intent, I start to vomit. Sooner or later I am going to learn that I physically can't kill my neighbor. The same process could be instituted on any evil to nip it in the bud. If instituted universally and consistently, these limitations would then seem as natural as not being able to fly like Superman or to teleport.
Can an omnibenevolent God allow *any* sort of Hell--a place where those who refuse to accept him as Lord will dwell for eternity?
The concept of an eternal Hell only seems to be relevant assuming Christian eschatology is accurate. For if there is no ultimate end point to the world as we know it, and no rebirth into Heaven (or into a sinless physical world, depending on your belief), which will last from then to eternity in perfection, then there would be no need for a Hell to cast the rejects into it for all eternity. Yet even in that assumed construct, the concept itself goes against several tenants of love:
Love is patient, ergo, God should be patient with us, given our limited timeline, limited knowledge, and limited comprehension. On an infinite timely, anyone would be expected to arrive at the truth, but truncating that timeline and making the judgement binding forever means that God has limited patience.
Love is kind, ergo, God should allow conversions at any time, because to lock someone to a fate decided by their own imperfections is not kind at all.
Love keeps no records of wrongs, ergo, God would have no justification for making an eternal judgement of that nature. (It also means that Jesus didn't need to die for our sins! But that's another story...)
Love does not delight in evil, but rejoices in the truth, ergo, God should be simply happy when any human chooses Him.
Love always trusts, ergo, God should trust that people will come to believe in and accept Him given an infinite timeline.
Love always hopes, ergo, God should perpetually hope that people will come to believe in and accept Him given an infinite timeline.
Love always perseveres, ergo, God should endure those who reject Him even up to the time of their conversion.
On a long enough timeline, love does conquer all, and truth prevails. :-)