How to prove the following language is not in R
Hint: This language is actually computable for every $c$. If $M$ terminates within $c$ steps, then it only gets to see at most $c$ symbols of its input, so in some sense its domain is finite.

There are some subtleties here. For example, it might be that there are also infinitely many inputs on which $M$ doesn't stop within $c$ steps. Perhaps it's better to first prove that the following language is computable for every $c$:
$$
L'_c = \{ \langle M \rangle \mid \text{$M$ stops within $c$ steps on all inputs}\}.
$$