[1] Which glue do you use to fix loose parts/unstable figures/glue figures to their bases?
I usually use the glue 'UHU flex and clean' - this glue doesn't 'fog' the plastic like some super glues
do - also, a small portion of it is enough already so there are almost no remains
which could decline the look.

[2] What do you do if your material starts to settle? (Aka if spiky things round off on their own)
I use a hand blow-dryer to get a stable first layer on the part I just made.
Usually, a few seconds of blow-drying is enough to prevent it from changing
it's shape. However, you need to experiment with your own material:
some need to be blow-dried with hot air, others only 'like' cold.

[3] Which materials/tools do you use for your own bases/figures?
Please take a look here