1. TM is an encoding of (0,1). but every encoding of 0,1 is not Turing machine. There might be languages for which TM doesn't exists(which are not REL).
2. (0,1)* is countable (can be enumerated in increasing order of the size of string like epsilon, 0, 1 , 00, 01,10,11...)
3. As TM implies encoding in {0,1}, from point 2 as encoding in 0,1 is countable, set of TM is also countable.