I can not answer all of your question here. I just recently rebuilt my toilet. My waste cast iron drain pipe was damp on its outside, so I knew I was leaking somewhere. I disasembled my tiolet, by removing the two base bolt nuts that you mentioned.
Of course I shut the water off first, disconected the water line to the tank, and emptied any water left in the bowl and tank.
After the nuts were removed from the base I carefully lifted the toilet (its still heavy) and noticed the wax ring around the hole to the drain was old and not in good shape. Water was getting around / through the wax ring ( a $6.00 item). I reset a new wax ring, and with help guided the tiolet straight down on top of the ring and screws. Reattached bolts and water line, and was good to go. My tiolet was more secure to the floor, and the seal stopped the water from running down my waste pipe.
Also important... Do not over tighten the bolts on the base of your tiolet, you could crack your ceramic tank, and you really don't want to do that.
As far as the bubbling and water back up. IM going to guess you have described a clog and that is someone else's specialty.
Good luck and take your time, think about each step as you do it, its not that hard.
Tj
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