> How often do you need to check on your bees.
For the sake of getting good crops and managing them well, assuming Langstroth hives where you can pile on supers at the right time, maybe three times a year would be minimum. If you don't care about crops, never works. If you want to learn about bees, I'd say once a week...
> Are there any situations where you can plan ahead and get the hive set up so that you can just leave them alone for, say, 3 months at a time or so?
> Could you potentially kill your hive if you left them alone that long?
You won't. Something else might, but if you have natural comb and healthy bees and you haven't messed up the natural ecology of the hive, they should be fine indefinitely. Of course they sometimes swarm and sometimes that works out and sometimes they end up queenless. If they end up queenless, they will die out without intervention.http://www.bushfarms.com/beesfoursimplesteps.htm
> I remember finding big hives of wild bees up in small caves in the rock walls of the valley below our house when I was younger. Obviously they can survive on their own without human interference
Obviously. Yet there are those who don't believe that...
> but I also know that sometimes if you create an artificial environment (a wooden hive box) then possibly the situation might change.
Especially with artificial comb.http://www.bushfarms.com/beesnaturalcell.htm
>I'm thinking that to maximize the honey harvest, then collecting the honey more often will get them creating more.
Sort of. Certainly you can manage them for more production.
> But I'm wondering if you don't harvest it enough, will this somehow hurt the hive?
No. Other than them swarming, and half the bees taking to the trees...