Multiple files per partition/filegroup?
You can't work on the partition &lt;=> files relationship. Partitions are just affected to a Filegroup. However, splitting your Filegroup into different files will help with performance.
The numbers I always use is to have the number of partitions per Filegroup set to the MAXDOP value. I got this looking at how SQL Server split the tempdb into different files and I did notice some improvement copying this behavior.

Regarding partitions, what you should do is split them on filegroups so that the ones that are no longer updated never move. We typically have a Hot filegorup in our DWH, and a Cold one. The cold one is Read Only and we only change that status on the day we move data from Hot to cold. You could do this without having to create one filegroup per partition. That just makes it harder to manage.