1) It is strange that provider id variable is not included in provider data and client data. It may have a different name and usually is labeled as "provider serial number".

2) yes, if you are merging provider data into facility data, you are dealing with one to many merging. In this cases, facility dataset is the master file and provider dataset is the using file.

3) Without access to the ESPA data, it is difficult to figure out the problem.
Please note when you merge provider data into facility data, the number of cases(facilities) in your master file (facility dataset) will proliferate because multiple provider records are associated with one facility. Maybe this causes the nth value no longer the same?