I've read about branches having internal stresses and twisting/warping.
The main reason not to use wood from branches normally is that it's full of reaction wood, wood that has internal stress from its original orientation of the branch where it was under stress, supporting the weight of the branch and its foliage. When the branch is sawn into planks the release of this stress can lead to very bad warping.
Note: this is not to say you shouldn't try to use branch wood. There is much fine wood wasted because it was originally in a branch, but you'll never be sure how much it might warp. However confine yourself to smaller pieces and work in stages to your final dimensions and often you'll have few problems.
would there be a huge difference in how I should treat the wood between cherry/pear?
No I don't believe so. I think you can treat most hardwoods and fruitwoods equally when it comes to drying out pieces like this and get approximately the same results.
Is this a problem if they are cut into small cubes as appropriate for an end grain cutting board?
I don't think so:
But obviously make sure the wood is fully dry (or seasoned) before you use it.
Since the pieces will be small pre-glue, do I still need to let the wood cure for ~1yr? (I've read that green wood should be cured?) If so, should I leave it in long square sticks to cure, should I just leave it sitting in the compost pile for a year or should I cut it to cubes and then leave it to cure for a while?
Definitely don't leave it in a compost pile! Leave the pieces as-is (I think this is referred to as "in stick") to dry before dimensioning and glueing. They can be dried outdoors (off the ground and under cover) or in an airy space indoors (e.g. a well-ventilated garage or covered porch).
As for how long to wait, there is a rough rule of thumb about drying green wood given out a lot online, saying to allow one year per inch of thickness. While this is for hardwoods specifically (a detail often left out when the phrase is repeated) and obviously will vary somewhat even among hardwood species it is a good conservative timescale to have in your head for any drying.
Further to this I would say myself, wait as long as possible. It's almost never a bad thing to wait longer when drying wood compared to doing the opposite — in normal circumstances wood can't be over-dried, but it can most definitely be under-dried!
For future reference if you get a chance to acquire wood like this, you want to cut it up into the pieces you'll be drying and immediately coat the end grain with something to protect from cracking. Don't be complacent and wait until the following day or later in the week, you can start to get cracks forming in just that little time. The goal is to prevent the formation of cracks entirely, not halt them spreading.
The best thing to use for sealing end grain for the DIYer is melted wax, which should be applied liberally. Any solid wax will do, from canning wax to virgin beeswax to random bits of old candles.
Don't rely on "latex" paint for this. Despite how frequently it's recommended online for this purpose it's a bad choice as it's a terrible water barrier. The only reason to use this type of paint would be if you literally had nothing else on hand that would do the job better. In the absence of wax things that would work better than "latex" paint include enamel paint and varnish, both of which have good water-resistance. But they must be applied very thickly for best results so multiple coats may be required.