Can we find a Turing machine such that there is no Turing machine to decide whether it halts on $\epsilon$?
Suppose you had such a TM, namely a machine $M$ for which the problem was "Does $M$ halt on empty input?" Certainly that problem would be decidable: one of two algorithms must be correct, (1) Answer "yes" or (2) Answer "no". The fact that we might not know which one is the correct algorithm is immaterial here; the only thing that matters is that we're sure one of the algorithms is the right one, so we know the problem is decidable. In more general terms, any decision problem with a finite number of instances is decidable.