DT's absolutely correct in that the red one will be much faster - kinda goes without saying.
As for your questions:
1. The 2nd gear popout issue is WAAY overblown. Yes, on 2003 and newer cars, you don't have to worry about it. But, if a 2001 or 2002 had it, it would likely have been fixed by now. And, most often it can be fixed with an inexpensive repair. Yes, it is possible to still see one in the wild with the 2nd gear popout issue and it is possible that it could require replacing synchros to fix. But, I'll bet you'd have to look at 100 cars to find one with that problem.
2. Changes 2001 to 2003: as B3 states, 2003 and newer will have the MOST system for the stereo - not necessarily a good thing (harder to modify if you want to upgrade to a newer, better system than a 15 year old one); you will get a glovebox on 2002 and newer cars, and slightly (very slightly) nicer interior. Starting in 2002, you could get the X50 power kit on a car, but, again, as B3 states, neither of these has the X50. Plus, it is very easy to tune a non-X50 car to produce more power than an X50 car, which is more power than you'll ever need. The 2005 only "Turbo S" is really just a 2003-4 model with both the X50 power kit and the PCCB brakes. They normally bring a big premium, just because they are rare - not because they are better. That's about it. Frankly, there simply isn't much of a difference between a 2001 and a 2005 Turbo S. With the same miles and condition, though a 2001 will be cheaper than a 2002-2004 model which will be cheaper than a 2005 Turbo S. I would not hesitate to buy any model year of 996tt - just make sure you pay a market appropriate price.
3. Coolant Pipes Pinning - It can be done with the engine in the car, but almost everyone has it done with the engine out. Why? Well it is easier, but more importantly, it is considered one of the things that can wait until you have another service that requires dropping the engine. If you don't track the car, then don't even worry about doing it. If you plan to track the car, then you'll want to have it done, but it isn't like an IMS bearing where the price of failure is a blown engine. If your coolant pipes come unglued, then you'll lose coolant. If it happens on a track, that will end your weekend and can be a hazard for the other racers, so guys who track their cars get them pinned. If it happens on the street, you pull over and have the car flatbedded to your nearest shop to have them done, but it is very, very, very rare that it ever happens on the street. If you have 2 identical cars, and one is pinned and the other isn't, then I would consider it a factor. Oh, and by the way, now, the standard for this repair is to have the coolant pipes "welded" into place rather than just pinned as the pinned pipes can still leak. So, pinned is better than unpinned, but the hardcore guys are going to tell you that you still need to have them welded.
One last thing is that you are likely to never "lose" a dime on either of these cars. If you pay an appropriate price for a 996tt, then at this point on their depreciation/appreciation curve, you are going to get your money back come selling time (assuming you've kept the car in good condition). So, the cost involved is maintenance, which you'll have with any car. Over the past nearly 3 years since I've had my 996TT, it has been the cheapest car to maintain in my garage. So, in choosing between a higher-mileage car with questions re: maintenance and a lower-mileage car with known good maintenance, it is probably cheaper in the long run to buy the more expensive car.
2002 996TT X50, Guards Red
1987 928S4 Guards Red
1987 951 Guards Red
2006 955S Arctic Silver
2006 955S Lapis Blue
Gone but not forgotten: 1999 996 C4 Aerokit Black; 1990 964 C2 Guards Red