I don't know what version iPad you are using, but I have three: iPad2 and mini iPad are both at version 9.3.5 and are "up to date". Maybe they don't update any further, I really don't know. But I usually used the iPad 2 and was having so much trouble that I thought it was going kaput on me. So .... I recently went and bought an iPad Pro, which is at version 10.0.2 now.
If I think back, some of the problems you are having are very similar to what occurred for me. I often could not even get the reply box to allow me to type. Cursor invisible, pages would hang ( not just here), paragraphs did not separate although they were typed as paragraphs, could not go back and edit -- the box would never come up, etc . I blamed the ipad, because I did not have the same problems on the PC. Since getting the Pro, I don't recall any glitches lately.
Anyway, most of the times I have problems here, it is with an ipad, not PC, so I "think" there must be an issue using tablets that is intermittent, as you have so well explained. Sorry that I don"t have any helpful tips for you.