50/50 is pretty much standard in FL for physical and legal custody. It's what a court would award.
Medical insurance is typically pro rated. You should be paying 36%.
Child support would be minimal and yes, he could easily stretch it out for a year, after child support would end. You could get it awarded now if you move out with a temporary hearing, but you would need an attorney. It would probably cost more than the total support you would get.
As for the house, how much equity is in it? That's the key as to whether it's worth $3000 or $5000 or whatever it may be.
Furniture and other materials items need to be clarified now, otherwise you would have to go back to court later to get anything.
I wouldn't sign anything unless the dogs were 100% written to me. I I have dogs. I wouldn't give them up for the world!
Make a list of what you need changed to agree. It doesn't sound like the 2 of you are that far apart. Once he reads it, it's possible to mediate yourselves at your kitchen table.
Your requests are for the most part, reasonable. If he won't agree, you will have to hire an attorney if you want better results. Come back when you have more info. Thanks.