Not sure what you know, or even if you have a second bathroom to use, but Fairview may be right, up to a point. If the floor is rotten, which it probably is, The toilet has to come off, the old floor has to be cut out where damaged up to the joists, nailers have to be added to the joists, and blocking to the floor, and the floor replaced with minimum 3/4 inch plywood. We are talking about carpentry work, and I would do what I could to make the job easier for the plumber. The toilet HAS to come off, so I would accomplish this task first. It sounds like you may have an old toilet that should be replaced, but we don't know that, as you have posted no pictures.
The only toilet I have used in the last several years is the Kohler Wellworth, and they have given me no trouble at all, but there are other good ones available.
Once you get that toilet off and stick a big rag in it, and we can see the floor, maybe we can help. We cant now.
If you are the squemish type, and well off, just call a plumber. Some people cant even stomach the sight of the old wax.
Changing my Kids Diapers never bothered me, the way I see it is S**T is just another part of life. Gross but true.
Just figured Id let you know what you are in for so you dont bite off more than you can chew :laughing::laughing::laughing::laughing::laughing: