1. Can a Bavarian supply train supplies a French general?
No; has to be the same color supply train (third item in section 9).
Arenberg is the one exception, as he can be supplied by the Prag supply train. (section 22)
Eon Lee wrote:
2. Can a general eliminates it's own supply train? (like while retreating)
Definitely not; see the third bullet under the second item in 11.2.
Never during retreat (which is why you should avoid blocking your generals' potential retreat lines with trains), but during the movement phase of your turn you can voluntarily remove a supply train from the board and immediately place it at a friendly major fortress for 4 TC. (section 10.2)
More explicitly, I would like to answer your 2nd question: No, a general cannot eliminate his own supply train. However, you may take the ST offmap during your movement phase. (Note that during retreats, you cannot eliminate any supply train!)