Manual shifting & Injuring a Car's Function

We bought a preowned 2013 Fiat 500 Pop with 22k miles on it.  I grew up
driving sticks and have always enjoyed and preferred driving manuals... With
that said my husband has never driven a manual and trying to teach him has
been a little tough on my nerves.  He has accidentally went into 3rd instead
of 5th twice and revved the car for what seemed like ages.  He is sloppy
with the clutch and I don't trust he is pushing the clutch all the way IN..
When I'm in the car helping him remember the steps he does not do so bad.
He gained confidence and drove it to work yesterday and returned with the
a burnt clutch smell. I have not let him drive it since, because I have felt a
few changes in the car, and i need help finding out if we could have
damaged the car.  
I was averaging 33.7-41GPM and the car felt solid and steady.. After his
attempts at learning I cannot get the GPM above 31.7gpm and its doing
worse on the HWY instead of the 44gpm I had been able to accomplish.  
Also, now when I'm in red light in neutral I feel like the car is more shaky and
less steady... The clutch smell is still around and its been 2 days of
meticulous shifting.. How can I know if something has been damaged? Are
all these things my imagination or is the lesser mpg, shaking and smell a
true indicator of damage?  
Thanks a lot.

Carmen