If I create targets for this but I underestimated my expenses, do I adjust the targets? I have the available funds to cover the extra spending. Conversely, if I ended up underspending for a category, do I lower my targets?

I could totally be wrong about this - but my understanding is that targets are just for reference. It's just to help you make sure you're assigning enough money for things you need.

Nothing rolls over to the next month? As in, if I overspend a category in Jan do I need to assign for the deficit in February?

You don't need to bc YNAB forces you to cover the deficit in Jan from another category. You can't punish a category. It's very intentional.

So balance the categories but I still have the option to modify targets if I feel it is justified?

Yes but you'll do it in Jan not Feb.

@mysterious-tomato-10057 is correct in that you have to cover overspending in the category by moving over money from another category and that is separate from targets. As far as targets rolling over - I believe that depends on what kind of target it is. Some do, some dont

Everyone is giving you good info here. Targets are just for you. If you over spend, then you’ll need to cover that from the current month, if you find you are consistently overspending you should adjust the categories. And vice versa if you find you are underspending you can adjust them as well.