Try Super Sculpey:
it can be baked and thus remain hard
Yes,
but if it has been liquefied, there are limitations as to the number of times.
135 degrees C.
Plastiline:-
it was specifically developed for this purpose unlike other products with similar names!
Paddle rollers,
masking tape,
brushes
are available- see the full range
Try Super Elasticlay;
it remains flexible even after baking
Yes -
use Sculpey diluent.