Slow Mac mini (mid 2011) no hardware issues, no software issues
It sounds like a lot of the speed problems you're having comes from running newer software, macOS 10.12, that usually requires more system resources on a computer that has insufficient RAM (2 GB just does not cut it practically) and a slower HDD. However I don't think that would normally cause quite the amount of speed reduction as you have reported.

Nevertheless, for a quick speed boost, I would definitely recommend upgrading to 8 GB of RAM. Apple has information on how to upgrade, just make sure that the RAM you get is compatible with Apple's specifications. For example an 8 GB RAM kit from Crucial should work.

Additionally, I do know that HDDs can be a speed bottle neck, especially as they get more full and are older. You can upgrade to an SSD (here's a guide by Crucial), however that is a far more complicated process, and you will also need to transfer all your software from the old HDD.

But your speeds are very slow, so there is probably some software problem. You can try to diagnose that by going to System Preferences > Users &amp; Groups > Login Items and see if you have programs loading at boot. Also if you can check Activity Monitor, that may show if something is using a lot of your CPU. In the end, you may need to do a backup, wipe your hard drive, reinstall macOS or an older version of OS X, and transfer your documents and settings.