Congratulations!
Check everything is tight, and lubricated. Check tire pressures every ride. Wear a helmet. (Threw that one in for good measure, mine has saved me)
Tire life depends on the tire construction, pressure, and what it is rolling on. Tires are worn out when you start to get a lot of nuisance flats, usually because the tire is too thin. I have 1500 km on my kevlar-belted Bontrager Hardcase tires, and they are good for a lot more. I have Continental 4000 25C tires on my tandem, and they are reputed to last very well, but I don't have enough km to know yet.
Wheels need to be checked for trueness (runout), and broken spokes. If they are true, and the spokes are tight (these two go together) then they are fine. Spin the wheel and hold a spoke key or metal against the spokes, listening for any that sound different.
Chains are not a simple answer. Everyone has an opinion, and there is no right and wrong. I used to use lots of lube, often. Now, my road bikes don't go out in the rain so I use a dry wax-based lube and add it every second ride. Much cleaner. Chains are worn out when they are stretched. You can buy an inexpensive pitch gauge that tells you quickly, or you can use a tape measure (which is a hassle). If they are worn too far, you will have to replace sprockets at the same time. Get them early, and your sprockets may still be good. See the link for instructions.
Can't help you on the carbon, I am 6'4" and have never had a seatpost that was too long. If you are cutting carbon there is a right way and a wrong way, IIRC. Ensure that there is sufficient length in the seat tube. Seems to me that a carbon seatpost is pretty light, not much weight to save.
For basic maintenance, you might want to read Sheldon Brown. Sort of a grown up hippie cyclist, but some good articles, very down to earth. He has articles on tires and chains, among others.
http://www.sheldonbrown.com/home.html
Jeff