How to find out what are accept, loop and reject in this Turing Machine?
Yuval's answer applies to your machine T$_2$. With his assumptions, we have the following behavior for your T$_1$ on possible inputs:


It will reject the empty string, since there is no move defined on the "blank" symbol.  
It will not accept any string consisting only of $a$ characters, since it won't reach the HALT state.
It will accept $a\dots ab$, since it will reach the HALT state.
If the input is a single $b$, it will enter the HALT state and will then fall off the left end of the tape. Whether that should lead to acceptance or rejection depends on your definition of "accept" and "reject".
Whether it will accept a string like $aba$ or $abb$ will depend on your definition of "accept", since in these cases it will enter the HALT state and will never process the characters beyond the first $b$.
There is no loop state, at least under Yuval's and my interpretation.


You need to look closely at your local definition of a TM, since there are several forms they might take and of course we have no way of knowing what definitions you're using.