Can I use my Apple ID on another Mac?

Here's the deal: I have a Mac Pro that I use at home with my own, personal Apple ID. I want to buy a Mac for my business and want to have two user accounts on there. One for the business which will have its own, separate Apple ID, and one for my personal use that will have the Apple ID that I use at home on my Mac Pro.

So can this be done? I'm guessing it can be done. But the thing I really would like to know is, can I use the apps that I have purchased on the Mac App Store from my own, personal Apple ID on the business Mac? If so, would they only be accessible from my personal user account or the business user account as well?