Is it possible for the Bitcoin source code to be altered to the point where it can adopt the benefits that a lot of the other alt coins supposedly have (better security, faster transactions etc)? Or is that fairly unlikely now that the coins are already mined and out there?
I'm not aware of any alt-coins that have better security than bitcoin.
Bitcoins transactions are typically less than 3 seconds in trust situations. There are plenty of other ways to deal with trustless situations.
I don't see any benefit from any of the alt-coins. They are almost all bitcoin copies that offer no significant improvement.
Certainly, if there was a need, bitcoin protocol could be altered. However, it would require near unanimous consent of all users.