Yes, I would keep rental money in its own account, even if it is just one account for all of your rentals at first. When rent, repairs, and personal spending flow through the same account, it is hard to tell how a property is really doing, and it is even harder to sort out later. A separate account gives you a clean trail: rent in, expenses out, and a balance you can check without guessing. If you grow, you can move to one account per property or per group of properties, and still tag every expense by property. I would also keep security deposits handled carefully under your local rules, and talk with your accountant about the setup that fits your situation.
One operating account per owner/LLC, not one per house. An account per house sounds clean but you end up moving money between them every time one house has a big repair.
What makes one account work is tagging every deposit and every expense to a property the day it happens. Then each house still gets its own numbers.
The one I'd add: security deposits don't belong in the operating account. They aren't your money until move out, and if they sit with rent they get spent. I rent by the room so there are a lot of small deposits, which makes that matter even more.