When I say upper slot: Looking at the inside of the Mini that would be the first one that you can touch right under the wireless antenna grid. You can reach in, disconnect the cable and pull the drive out. What I did was use carbon Copy cloner and cloned the stock hard drive to my SSD connected in an external enclosue. Then I swapped out the drive. You can install the original drive in the lower slot, and the then erase it and call it Time machine. Then you could use it for that. The trim program Apple uses only works with their SSD. Using the free Tim Enabler program that you can download will enable trim on any non Apple SSD. You should not have any issue using it. It is like an app and you just turn it on or you can turn it off if needed.
Here is what I did on my Mac Mini late-2012 using iFixit's (iFixit.com) dual drive kit.
I took my 500GB HDD and placed it in the supplied bracket which would be the "upper slot" (under the logic board - furthest away from bottom opening). I installed an SSD (Intel 520 120GB) in the "bottom slot" (closest to bottom opening). I did this because with Mountain Lion 10.8.3, the GUI Disk Utility will see the two drives and mark them as needing to be fixed (highlight in RED). When the FIX button is pressed, Disk Utility automatically creates a Fusion drive (logical volume group) and the 1st drive it will pickup is the one closest to the opening (bottom slot) then add in the drive furthest from the bottom opening (upper slot). This mean we want the fastest drive to be selected first (SSD) and the slowest 2nd (HDD). If the drives are in the opposite positions, then the automatic Fusion drive will be setup with the HDD then the SSD. Apple's factory implementation of the drives is as I explained intially SSD - bottom slot closest to bottom opening and HDD upper slot. I used Internet Recovery (Command+Option+R) then the GUI Disk Utility as I wanted a Fusion drive setup. I Reinstalled OS X from the OS X Utilities menu. After OS X's install and during setup, I migrated my user account/apps/data to my Fusion drive.
If you want to use the two drives independently, you will need to use Terminal and diskutil commands to format the drives so you can use them independently. The GUI Disk Utility will ALWAYS show the two independent drives as needing to be fixed and configured into a Fusion drive.
Terminal diskutil commands to format and label a drive.
diskutil eraseDisk JHFS+ Primary /dev/disk1
Where "Primary" is the label for the drive (e.g. Macintosh HD) and /dev/disk1 is the slice to format.
Regarding TRIM, there is no need to enable TRIM in OS X for 3rd party SSDs (in my opinion). Newer drives have garbage collection and that feature handles the efficiency and performance of the SSD. My Intel 520 120GB has the SandForce controller which uses garbage collection and I don't have TRIM enabled in OS X and the drive performs great.