I went to a shop and asked to have the motor dropped in. The mechanic said there would be some problems with the distributor signals. He said the motor would run, but the performance is poor and wouldn't work properly. Is this true?

 

You obviously took it to a shop that knows nothing about swapping Honda/Acura motors. The distributor issue is simple: use the HF distributor. Definitely don't let them do the swap if you decide to go through with it.