Jetta'01 Auto Turbo with SO MANY problems/codes!

Hello! This is my first post and I need some help before giving my daughter's car away.

It has lots of problems and is actually:

1) Hard to start and the battery goes exhausted (it is new). I have to step the gas very down so it can start, but since the car isn't being used...
2) The ASR is on all the time.
3) It is shifting really hard. It jitters/bangs hard while shifting 1-2, 2-3, and less while shifting 3-4. The same happens while reducing the speed.
4) After the engine gets hot it beeps and the oil light stays blinking for a while. I noticed it beeps mostly while stepping the gas.
5) Engine light is on at all times.
6) The break sensor light is on all the time.
7) while in idle if I step the gas at about 2K, I see lots of smoke coming out of the muffler exhaust pipes - smoke is sort of grayish but doesn't smell like oil burning.

It runs ok on the freeway but I don't think it is not running/speeding strong - maybe the 5th gear isn't coming.

I took to Advance Auto and they gave me the following codes:

P0341 - Camshaft position sensor A
P0102 - MAF sensor
P0030 - O2 Sensor
P0135 - O2 Sensor
P1780 - Generic Global code (x2)
P705 - Transmission Range Sensor

This is what I tried so far:
1) I replaced the TCM for a used one but continue having the same problem/codes.

2) I tried cleaning the MAF with the cleaning spray with no results.

3) I took it to a local trans mechanic and he told me he can reprogram the computer to adjust the shifting problem - is it for real?

I really do not know where to start!

Thanks for any input! :)
Gil