cliffcoggin

https://www.ebay.co.uk/itm/285098951418?fits=Car+Make%3AAudi|Model%3AA3&hash=item426138c2fa:g:LM8AAOSwP8djtoa0
I have never done it, but for seven quid it might be worth trying.

To be sure I understand the question, are you saying that:
- ignition is off,
- first gear is engaged,
- handbrake is off,
- car rolls downhill in jerks.
Is that correct? If so, that is exactly what I would expect. The jerkiness is caused when each piston arrives at TDC (top dead centre) where compression is at a maximum, hence resistance to motion is at a maximum.
If I have misunderstood please give more detail.

If the car genuinely has a TPMS there must be a reset switch or menu item. Therefore either you have not found the reset, or there is no TPMS and the warning light is false.

Alastair.
I have no certain knowledge of those clips, but I don't believe Audi would add to the cost of the car by fitting them unless they were necessary. When every penny of manufacturing cost has to be justified to the bean counters the design engineers must have had a good reason to fit them.
I also don't understand how the clips got into the sump. Clearly they were not fitted correctly to the rockers by whoever has had that engine apart in the past, but I don't recall a passage between head and sump large enough for the clips to fall through.
Of more concern to me is the fact that the engine has been run without lubrication, a potentially destructive operation. Have you driven the car yet, and if so how does it sound and what is the oil consumption?