Q on managing category page with a LOT of items

I'm starting to get some categories with 20-30 listings, but since it's adding 10-20 listings a day, those categories are going to grow quite long.

Is there a good way to manage category pages with hundreds or thousands of individual posts, either by introducing some sort of pagination or otherwise? Is this built into the theme or do I have to code it in myself, and if so, how do I do so?

Can I also post a calendar widget and have it only apply to the currently viewed category?