Being a shop owner I understand the need for deposits. I think I have asked for about ten deposits in twenty-three years for repairs on cars we had in our possesion. These would have been for repairs that exceeded the value of the vehicle and it was a first time customer.
We do also ask for deposits on special orders.
If its been there three weeks and they have no answer yet I would say that they aren't interested in your business or they are very busy. Unless they offer special services I would find someone less busy and more eager for your business.
I deal with a machine shop that takes 2-3 weeks to repair cylinder heads and we only use them for work that I would only trust to them. The reason they are so slow is they are that good. They make reliable mmachine repairs to heads that others would throw away.
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician