You don't need to screw anything to anything. Dry fit the bath into it's final place and make sure everything is level - length and breadth and then move it back off the baton(s) then use (good quality) silicone to set the whole bath with the under edge baton onto the fixed wall baton with the steps I mentioned earlier. Then fill the bath full with water, screw the feet down and leave for 24hrs, one it's all set and the feet screwed down, the bath won't move, doesn't need any other kind of fixing.
That gives you 2 seals, one underneath and one along the edge, the final wall covering goes on then the top seal is applied, ending up with a 'triple' seal. Just pay careful attention to the 'wet' corners and edges so the silicone has no gaps or air bubbles.
Not an issue, again it's not to hold much weight, rather to offer a platform to support the short edge from moving/flexing and allows a place for the silicone to be seal to the wall and the bath properly. Cut 2 sections of baton for the short side, one into the back corner, then as small a gap as poss where the taps/overflow will live or use a narrower piece, if it's a normal bath setup, then a short section to just inside the outside edge to allow for the bath panel but will help support the outside edge.
Yes, a line of silicone behind the baton onto the wall will help secure it, no reason not to.
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