Yes, the states are set up correctly. However on your input setup, you need to be able to go back to idle state when you let go of the key, right? Use a "get key up" action and use that to move back to idle state in both left and right. with your current input setup, you can not switch from walking LEFT to walking RIGHT either, before you let go of the LEFT key. I suggest connecting the LEFT and RIGHT states aswell, and also listening for key input to change direction there.
What i mean is in your left state you will listen for button RIGHT and if buttong RIGHT is pressed you will go to the RIGHT state and vice versa.
This makes movement feel better as you can switch between the 2 states without having to go back to idle state first.
Now for the animations - What you have done looks correct. In the left and right states in the INPUT FSM, as i stated in my post above, you should use the SEND EVENT action to send the correct transitions for the left and right animation states in the animations FSM.
Here, You should also make a global transition for the idle state so the character can play idle animation when the INPUT FSM is in the idle state aswell using the same method
Hope this is understandable - If not, let me know and i can make an example for you!
-Koz