Yes, there is a way to price it out. The DMG contains a downtime activity for constructing a stronghold which includes various types, prices, and construction times. On the same page, in the previous section, there is also a guide showing the expenses related to maintaining various properties- including all of the items mentioned in the building a stronghold downtime activity! That table shows the staffing you'd need of both skilled and unskilled hirelings to keep it running. The daily wages for each can be found in the PHB under Services in the equipment chapter.
- I do not have the books on me atm. If anyone would be so kind as to edit this to provide page numbers, it would be appreciated. Otherwise, I'll add them when I get home.
No, there is no rules structure system which provides regular income capable of reliably sustaining any type of property. There is a good reason for this: the whole point of D&D is to go adventuring. If you can just make money arbitrarily and rule over your land in peace, there's not much reason to go dungeon delving. (Unless your DM is fairly creative and dumps adventure in your lap everywhere you go) That said, there's plenty of roleplay based ways of raking in regular income. For example, if you manage to earn yourself a landed noble title, in a feudal medieval setting you should have the right to tax the people. Or you could blackmail a noble to pay tribute. That could sustain your property while you're out slaying dragons. You need to work with the DM on this kind of thing. Make sure that the whole point is to get your character out adventuring again rather than fidgeting with his finances to sustain his property.