I don't think the bolts holding the toilet to the floor would have anything to do with it, unless the toilet is sliding all over the place and the waste pipe is no longer sealing (very unlikely IMO). I think water will be tracking down from further up.
yup I mean the doughnut washer that is under the cistern that seals between the pan and the cistern. If you don't have a concealed cistern that is. They are normally quite straight forward to remove providing you can isolate your water supply and unscrew the two wing nuts holding the cistern on to the pan. If you only have one toilet and worried about not having a loo, worst case scenario if you just chuck a bucket of water down the pan when you need to flush it.
Odd about the lid not coming off, can you see silicon holding it down? I think sometimes the push button on some units holds it down too, can't quite remember. My push buttons are not holding my lid down.
*edit* ah this is the vid I saw ages ago. Pulls the siphon out with it if your not careful which could be why yours didn't want to come off.
https://www.youtube.com/watch?v=fIKRaSzvo0w&t=33s