I'm not sure what that first sensation is, but I did have some luck putting lube in ahead of the dilator (I got a yeast infection kit and used the applicators for lube instead).
The second question, yeah, that's normal. The lube tends to be scraped off at the entrance of the vagina and then it liquefies at body heat and drips down to go everywhere.

It probably isn't "in" your butt so much as all over it, but that can be hard to tell apart. I would find lube halfway up my buttcrack as well as on the anus itself. (Also, a fistula would not lead to the vaginal contents ending up in the butt without ALSO having some of the obvious symptoms that you list.)