A new SSD, out of the box, is not formatted.
You will notice in Disk Utility, under the model name of the drive- it says "uninitialized", and your first error when booting also says "disk...was not readable...". Everything will be good after you "initialize", or format the drive.
Use the Disk Utility. Erase, using Mac OS Extended (Journaled) format.
I don't know what is wrong with your bottom slot. Try a good NVRAM reset. Try that, using these steps.
Power off, and leave power unplugged for now.
Fill both memory slots - put one 2GB in that bottom slot, and a 4GB in the top slot.
Plug in power.
Press and release the power button, and immediately hold Option-Command-P and R.
You should hear the normal boot chime sound.
Continue to hold those same 4 keys until you hear the boot chime 4 more times. Some refer to this as a "deep reset". Release the keys after that fifth chime, and hold Option to select your boot drive.
Boot normally to your system, then shut down, using the shutdown command in the Apple menu.
Unplug power again. SWAP the memory, so the 4GB is now in the bottom slot, and the same 2GB is in the top slot.
Try to boot, while holding the Option key, so you should get the boot-picker screen.
If you get there, and you can choose your boot drive, do that, let it continue to boot. You should be good now.
If not, and it starts that beeping for you again, then, I suppose you get to use this mini with only 6GB - which is still better than 4GB - just not what you want.
You could try one 8GB stick, just to see if THAT will work in just the top slot.
I doubt it is supported, but then I have not heard of anyone trying a single 8GB stick..