Filemaker 12 can not read a fp7 file. When 12 open a fp7 file it converts to fmp12 and makes a new file. You will have to use 11 or 12 not both.
There can be only one instance of Filemaker sharing on an operating system.
There is a possibility that a virtual OS (VMWare, Parallels, Virtual Box, etc) could run a second sharing instance on a single computer.
I do not know. It might be cheaper to buy a used Mac for the single user...
If your older mac only needs a "read only" level of access to the data, you may be able to set up a system that exports the data from FileMaker 12 into tab, csv or merge files that are then imported into FileMaker 11. That has very obvious limitations to how useful this can be, but it's the only real way to "share" data between the two versions.