Hi
You have definitely given this alot of thought which is fantastic. Some answers to your questions:
* Size of house......... doesn't matter . The fact that you have a small garden in which he/she can sit out & relieve self is great........coupled with your wish to exercise the pet then that's perfect.

* If you rescue a dog, you are giving it a second chance at a happy & loved life. For this when you have gained the dog's trust, he/she will be grateful & return that love in spades!

* A bitch will not bleed after she has been spayed.

* Just use common sense re letting dog off lead in open places. Some places don't allow this but usually have signs up saying so.

Good luck. x