Which paramenters change if you increase mast rake? Is this an appropriate instrument if you expect strong winds?

I generally play with mast rake only if I expect extreme condition-either way. If it's going to be very windy, I'll send the mast back a little. If I know it'll be light for an entire day, I'll send it forward a little. It's important to know where the baseline is.

Also, do keep in mind that changing rake will effect things such as spinnaker luff tension. I'm a stickler on proper spin luff tension and have to be aware that when I change the rake, the tension will have to be adjusted accordingly via the spin pole or up top with the bale setting.

I generally agree with your remarks concerning luff tension of the spin, but isn't it a good thing having it tighter us usual in heavy air?
I wonder how different mast rake affects the main, at least the angle of sheeting should change.

The mast rake won't change much about the main, seeing as it is attached to the mast and to the boom. The angle of the mainsheet gear will change a bit, but that will mostly affect the force applied to the mast that induces rotation. Obviously the angle of the whole sail will change.

The sheeting angle will change for both the jib and the spin. The jib you can adjust, the spin sheeting point and halyard point is fixed (haven't a spin that doesn't hoisted all the way to the bale). You can play with things to get the luff tension right (more pole bend usually), but because the halyard bale will move relative to the sheet block, the sheeting angle will change.

changes in mast rake may require changes in rudder rake as well

In theory yes. Never had to do it though.

on boats with daggerboards and boom, the rake has only a subtle effect. As said by others, it effects jib and spi.
There is an effect on the weather helm as well. On your A-cat, the rake is more or less the only possibility to adjust it (apart from weight balance of course). On a F18, you can use the jib to trim weather helm as well.
Question is, if you want to change weather helm with wind strength.

Cheers,

Klaus