gynnoch chi is the standard form. Variations include gennych chi, ganddoch chi. Stick with gynnoch chi unless you have a particular reason not to.

Most likely: 'Are you getting a car?'

If it was in a sentence such as 'Wyt ti'n cael mynd yno mewn car?' then cael has a sense of being allowed to do something:

• Are you allowed to go there [in a/by] car?

Nothing, it's fine. It is one of the accepted answers.

Just checked, and there was a typo in one of the answers - now fixed. Thank you for letting us know.