1) How does the Mode C get it's altimeter setting? As I understand it transmits in 100's only and is not conected to my altimeter.
They receive pressure altitude only from either an internal device (rare), a "blind encoder" box hidden behind your panel that has its own connection to your static air pressure system, or it can also be fed from an "encoding altimeter", but the setting on the altimeter has no effect on what they transmit. The blind encoder is usually the cheapest, and is stuffed up behind your panel somewhere in "traditionally" equipped aircraft. I can't speak for the G1000 or other glass panels, many probably have the data coming from the AHRS boxes, the do-all gadgets that they are...
It's actually encoded in bits, which are in a specific order called "Gillham Code" but most Avionics guys will call it Gray Code.
http://en.wikipedia.org/wiki/Gillham_Code
The number of available bits in Mode-C is low enough that yes, the resolution is in 100 foot increments. I went to look up whether the "perfect" calibration was to change over at the exact altitude, or if it happens "in-between", but I can't find that right now. Computers weren't powerful enough, and the amount of time needed to reply to a directional antenna/dedicated receiver for Mode C at a traditional "spinning antenna" type of RADAR array.
Ever note that the flat bar antenna on top of the primary RADAR concave antenna is slightly cock-eyed to the main antenna? That's because your transponder talks to that antenna, and it's slightly angled "behind" the other because it'll take your transponder a certain amount of time to respond to the pulse/interrogation from the primary RADAR.
2) When I fly I always set the altimeter to Field Elevation and then takeoff and ATC then gives me another setting. Why should I use their setting since I just calibrated my altimeter to tell me what my true altitude is?
Yep, use what ATC gave you, their computer is correcting all the transponders to that setting on their screen. The system is set up to correct everyone to the same "real" altitude so that separation is maintained.
Here's some fun for you: If the controller gives you 29.92 and you accidentally set 29.82, how far off the real altitude he wants you on, are you, and which direction, above it or below it? (And thus, how much closer to the aircraft he just sent under/over you.)
AIM 7-2-1 is probably also worth a read... as well as FAR 43 Appendix E and F, and there's this relatively new gem...
Amendment(s) published May 28, 2010, in 75 FR 30193
Effective Date(s): August 11, 2010
6. Amend §91.217 by redesignating paragraphs (a) through (c) as paragraphs (a)(1) through (a)(3), redesignating the introductory text as paragraph (a) introductory text, and by adding paragraph (b) to read as follows:
(b) No person may operate any automatic pressure altitude reporting equipment associated with a radar beacon transponder or with ADS–B Out equipment unless the pressure altitude reported for ADS–B Out and Mode C/S is derived from the same source for aircraft equipped with both a transponder and ADS–B Out.
Which means that if you thought you'd just plop ADS-B in your aircraft utilizing its own encoder, or a separate one, alongside your old blind-encoder or whatever... you won't... 'cause your "source" for the ADS-B Out altitude must be the same "box" as the Mode C or S transponder. Luckily most encoders in light GA aircraft have been standardized on the DE-15 connector for years, a 15-pin connector carrying 11-"bits", thus... there's some "extra" pins for ground, etc.
Check out FAR 91.217. Your encoder and your altimeter only need to be within 125 feet of each other on a 95% probability basis, and only tested with your altimeter set to 29.92 during the test.
Frankly a lot of this is "historical". The instruments and test gear to test the instruments simply wasn't very sophisticated when the system was first dreamed of and implemented. Most good shops will get you a heck of a lot closer than these minimums, depending on the age and abilities of your gear on-board. The RADAR separation standards were written with these inherent errors assumed on two aircraft, one low and one high at their certification limits, still having enough separation to miss one another in the sky.
Look up RVSM (Reduced Vertical Separation Minimums) info, for more reading on how more accurate modern equipment and especially autopilots (required to be engaged) allow for more altitudes to be used and reduced separation for busy jet altitude routes, like the Atlantic "Tracks". Only properly equipped and tested/certified aircraft can "participate".
Of course, the big iron also often have RADAR altimeters to tell them exactly how high they are AGL. A buddy who flies 777's said it was eerie one night over the Pacific to see the RADAR Alt drop to 2000' AGL. After a while, he realized that a 747 was assigned the FL two thousand feet below them, and was slowly overtaking them from behind. GPS/INS is so accurate these days, that the airliners are dead on their routes, and the 747 was a pretty big "target" for the RADAR altimeter for an hour or so until he finally puled ahead of the 777.
Fun stuff.