Turing Machine can accept Epsilon? No
Because when we telling turing machine accept epsilon, that means yes cases of TM is accepts nothing.
Means u can simply ask this question "Is TM accepts nothing?"
We can only check that if TM accepts a finite or infinite language . But how can we say if there is nothing as a string, then still TM accepts it. It can never be decided. So, TM accepts epsilon is undecidable or not even Recursive Enumerable.