There are some table features that Adobe FrameMaker has, and I'm trying to find equivalent features in InDesign. I hope someone can help me locate those features or provide workarounds:
1, No, InDesign has not such a function.
2. You can do it in InDesign with any text, so you can do it here: Create a text frame, write a text like "Continue on page ###" For the ### use the marker Nxt Page number and lay the text frame on a position where it is at least a little bit overlapping the main text string.
3. No, only paragraph styles can it.
Bring it to the Feature Request.