Get out your owner's manual and make a list of the items needed at 60k. If
there's anything you can do yourself, do it. Anything you could not (or
did not) do, have the dealer or other shop do. If you have another shop
do the work, be sure they use the proper fluids. If you have another shop
do the timing belt, be sure they use a Hyundai belt.
To say that failure to do the 60k voids your warranty is semantically and
legally incorrect. Your warranty covers defects. If a part fails because
you didn't do the required maintenance, that's not a defect. That doesn't
mean that if you failed to change your spark plugs at the proper interval
that the water pump isn't covered. It does mean that if you didn't change
your coolant at the proper interval and your water pump fails because of
that, Hyundai can legitimately not pay for those repairs. In most cases,
even if you didn't change the coolant, they'd cover it anyway. They'd be
most likely to not cover if the dealer found something actually wrong with
the coolant. But even then, it's usually a hard to make case, so Hyundai
often winds up making the repairs anyway. I recently replaced a
transmission under warranty which I believed had the incorrect fluid in
it. The position of the rep was that it wasn't worth the effort of trying
to make a case that he wasn't sure he would win.
The most likely problem with the fog lamp is the bulb, but that's no
longer covered by your warranty.
The paint warranty is for 3 years/36k miles, so that may be why the door
handle isn't covered.