Always on basic question
If I make a change to one server in an Always On situation - like say adding an index - do I have to make the same change to the other server? 


No, you just make the change to Primary (master replica) database which is writable. Rest other databases in an availability group are either read only or not accessible depending on if you have opened your secondary replicas for read or not.


  And if I do, is there a risk of the two servers not being in sync?


If the replica sync mode is set to Synchronous then it will always be in sync. If it is set to Async, then there it might lag a bit. In my experience, unless you have a very high latency, its always near to instantaneous for async replicas as well.

for few concepts, this is very detailed info that you will find on how it works.