1. I use M6 countersunk hex bolts, some use M5. Either is fine really. Assuming you're going into the side of 10mm HDPE, I'd say probably use M5s. Get the nuts off eBay if you need to. Alternatively, self-tapping wood screws hold things together excellently, but you don't really want to be using them for something you'll be opening up regularly, since the head goes bald and the hole you've put the screw into will get chewed up gradually every time you reinsert it. They're very space-efficient, though, so that's perhaps something to consider.

2. Short answer: no. If you're running your linac with the stock motor, it'll be brushed, so you could technically just switch it on and off with two RC switches (one for each direction). However, it's probably better to just get an ESC, because it means you can have forward and reverse on the same channel. You could use a double-pole switch on one channel and basically make it retract when it's not activated, but that means you can't really stop it halfway up. So yeah, I'd use an ESC.

3. 10mm is a bit steep. I'd aim to reduce it to 5mm or below if you can. That said, the arena floor is never as smooth as you want it to be, and it's not going to be the end of you if you're not going full-limpet. You just have to put more effort into pointing your wedge at the opponent.

4. Since you're relying on your wedge entirely for your weapon, I'd put a steel edge on it. It'll get chowdered after a few fights otherwise. You only need a few centimetres up the wedge I'd say. The point is just that the tip stays sharp. I'm no expert in this kind of thing, but let's say you have a 5mm thick steel (perhaps hardox?) edge. I'd cut a 5mm-deep indent into the edge of the HDPE, overlay the steel, then bolt through with countersunk bolts. See below:

Flipper Edge.png
There are other ways obviously, like using thinner steel and bending it over the edge of the flipper in two halves, but this was the best solution I could think of.