1. If you're buying from any dealer they would have already done the fix. If you buy private party then the only reason to do the fix is for the extended warranty, which is pretty great.
2. Transmissions are solid and have 0 issues on these as long as the services are performed. The manual tranmission has lifetime fluid, but a lot of people do a fluid change at 120k. I did and do notice a difference in shifting. The DSG trans needs to be serviced every 40k miles. If you skip this, bad things happen! Either have the dealer do it ($400 I think?) or buy VCDS and do it yourself, it isn't hard.
3. No issues with timing belts. Good to 130k miles. As timing belts go, not too difficult, but I would say not for someone that hasn't done one before. Replace the idler pulleys as well, dont cheap out! IDparts has a great kit for the timing belt. Don't forget, the motor mount bolts are torque to yield you should always replace these.
4. These cars have 2 major issues.
a. Intercooler icing - if you live in a climate that gets fairly cold in the winter, the
EGR will end up causing ice to build up in the intercooler. I live in Denver and
have had this issue multiple times this winter. VWs fix for this does not work. My
advice is to delete the low pressure EGR to solve this issue. I removed my EGR
system entirely. It will take longer to warm up your engine, if this is an issue for
you, get a frostheater. Mine has been great.
b. High pressure fuel pump (HPFP). These have been known to grenade and take
out the entire fuel system. Make sure to always fill up at high volume diesel
stations. I prefer to fill up at a truck stop near me. This will get you fresh diesel
and help keep your HPFP healthy. This is the main reason it's a good idea to do
the fix to get the warranty as it covers the engine, emissions, and fuel systems. If
you decide not to do the fix, I highly recommend the cp3 injection pump swap kit
from darkside developments. The cp3 is extremely reliable and no longer needs to be timed with the engine.