Hello, thank you for your question, I'm Dr. Dan and I'll try to help you.
I'm so very sorry for your loss I truly am, it must have been terrifying to see.
The last question is the easiest, yes she would float if she drown, all that is needed for this to happen is that she have enough body fat to hold her up on the water. In a dog it doesn't take much fat to do this so most dogs do float even if not overweight.
I would suspect one of two things happened, the odd part is that there was blood in her nose. This would sugget that she had an issue with her heart or lungs before she fell in the pool. Heart disease and pneumonia are common problems in this breed, and if she started coughing or having other problems near the pool and fell in, then she did drown but had other symptoms as well. The blood in the nose is what is odd here.
Likely she did drown either way, the main question is did she fall in and drown or have some other problem that caused her to fall in. The only way to know this for sure is to have an autopsy performed by a vet (called a necropsy). A look at the lungs, heart and nose will tell us if there was disease before this all started. From my perspective the blood in the nose has me thinking that she had problems before she feell in the pool. I hope this helps, if not please feel free to ask more questions.