The cost is based on the base tax + modifiers.
The time was... erratic for me in my game as Germany. It was definitely longer... in some cases. But I had one that went in about half the time (while the province beside it was the one that took longer). Though they were primarily colonial holdings. I'm not 100% sure what was affecting the coring time.
I used to run into it, but over time I just started to enjoy consolidating and building up what I have as well. I'm always looking for the next place to nab, but sometimes I also just go in to knock a big neighbour down to size (even if I don't conquer anything more out of it).