If the length of the string is divisible by 7:
1) Each string must be divisible by 7, this means that the strings of length 0, 7, 14, 21,.. are accepted.
Now, we can make a 7 state DFA to accept the language. Since we want the string with length 0 to be accepted, we make the first state as a final state.
Next, we can traverse on the first 6 symbols and make a transition from the 7th to the first state (which we marked as final) so that the string with length 7 gets accepted.
You can observe that all the strings of length divisible by 7 are accepted.
Here is the DFA.
2) Since the string must start with a 1, there are 2 different paths from the first state. If we encounter a 0 then DFA must go to a dead state.
Else, it must again accept all the strings of length 7.
The DFA is: