I can play on PC, but unfortunately my fingers don't work, so can only control the Mouse. I have a remote mouse app on my iPad but I don't know if I need a actual dedicated keyboard to play the game. Also will my saves carry over to different platforms?
So firstly, no, the saves don't carry over, but the saves don't matter at all between LiS, BtS, and Lis2. Not at all.
I played LiS2 with a controller so I can't speak to the controls with a mouse, but if it's like the first game, you make choices with the left or right mouse button, Unlike every other LiS game, though, there is for the first time time-sensitive questions that give you a countdown to answer when you're walking around some environments. They are the closest thing to requiring quick action in a series that otherwise didn't have it.
Actually, let me load it up in collectible mode and check to make sure that's how it works.
Edit: Okay, I'm not sure how you navigated the character around in LiS1, but it's the same in the sequel. Hopefully you can control them well enough! As to the few timed conversations there are, it looks like they use whatever up/down controls you may use for selecting answers. There are only a few of these, however, and missing them probably won't get in the way of the episode overall.
Also, IIRC there was a single interaction that had me mashing A on an Xbox controller. So that's there, FYI, without an option to make the QTEs more welcoming.
Just wanted to let you know about these things. If you enjoyed the first game, I can earnestly suggest you'd like BtS and the first episode of the sequel.