There isn't anything in the core rules about building ownership, but you (or your DM) can fake it in a good-enough way (at least, so long as nobody tries to break the game using such a ruling) by estimating off the equipment tables. You need three things: cost for building maintenance (or rent), cost for food, and (if not renting) initial price of the building.
In the equipment chapter under Food, Drink, And Lodging, a poor meal costs 1sp. I'm picking "poor" because no matter how much you have, you want to stretch it as far as you can to feed as many, right? So go with "poor". That price is assuming making a profit, so let's be conservative (on the "more expensive for you" side) and cut it in half: 5cp to feed an orphan. Maybe shave that down to 3cp, since they're kids and not grown adults eating at a poor inn. (This is really back-of-the-envelope stuff, not rigorous at all.)
We can do something similar for the rent/maintenance of the building: a night's stay in a poor inn is listed as 2sp. Let's cut it in half to 1sp to eliminate the profit normally involved. Since a normal poor inn can maintain the whole building on 2sp per room per night, we can be pretty sure that the 1sp per orphan per night will cover (sans profits) whatever costs are involved in paying rent or taxes, repairs, replacing bedding, laundering, upkeep of the non-sleeping quarters and so on.
Somewhere, between the price for meals and the price for rooms, a combined inn/tavern also pays for their kitchen, so we're probably safely in the black with our estimates. You probably don't need to maintain a stable like a normal inn, and you're not paying for the volunteer labour, so that makes the estimate even more likely to at least meet or exceed the costs of rooms and food.
Altogether, that makes it 1sp, 3cp to feed and house a single orphan per day, assuming one good meal every day (which is not far off the unfortunate reality of old orphanages). If you want to have them slightly healthier, but be able to take in fewer, make it two meals per day and double the meals costs to 6cp, for 1.6sp per orphan per day.
So, very roughly, you see how you can use the goods and services lists in the core book to get a gameable estimate of the costs per orphan per day. From there you can look at what money you've got stashed and what your incoming donations are, and estimate how many orphans you can house and feed at once on an ongoing basis.
As for the initial cost of acquiring the building, that the core rules don't provide anything even close to helpful for estimating. You don't have to worry about this if you find a willing landlord, but if you have to buy the building outright, this becomes a slightly sticky issue. If I was running this game I'd probably just play it out, maybe angling for the druid to find a donor with a vacant building. At worst I'd just name a price in gold and get on with it, while making sure that the players know that the price is particular to this building from this seller, and they shouldn't expect it to set a precedent. Maybe, like 100gp or something.