Are the RMI requests handled per process or per thread on the server side?
The short answer is that it isn't specified. The RMI specification says something like 'there is no guaranteed association between client threads and server threads'.
About all that you can deduce from that is that you cannot assume RMI is single-threaded. In practice you will have found that your RMI remote object can be called by multiple server-side threads at the same time. So synchronization is up to you.
This is the best sense I can make out of your question: I must say I don't know what the difference between 'per-process' and 'per-thread' actually means.