This is literally a meaningless sentence. I mean, I don't even know what it was intended to mean.
Is this correct? I would have thought that a agent drives, but a car is driven, so the autonomous would be used. For example: 'tiomántar deich gcarr'.
The structure of this sentence might have originated in Hiberno-English; see here and here.
Do planes fly, or are they only flown?
Why not "á dtiomáint"? If we use that for a door opening, why not a car driving?
ten cars are being driven
tá deich gcarr á dtiomáint - "ten cars are being driven"
tá deich gcarr ag tiomáint - "ten cars are driving"
Is "carr" more common than "gluaisteán" ?
Yes. gluaisteán is a bit like "automobile", technically correct, but a bit dated.