Can I replace my regular HD with SATA SSD (Samsung EVO 850)?

To start off you'll need to follow this IFIXIT guide: iMac Intel 21.5" EMC 2544 Hard Drive Replacement to swap out your current 2.5" HD for the Samsung 840 or 850 EVO SSD unit.

Frankly, I would leave the HD alone here and instead install the PCIe blade SSD. Here is the IFIXIT guide to do this: iMac Intel 21.5" EMC 2544 SSD Replacement. The Samsung 850 PCIe M.2 blade SSD will not work in this system. You'll need either the custom Apple Blade SSD or this one from OWC: SSD upgrades for late 2012 iMac's.

In either case you need to be very careful removing the display assembly as it is very easy to damage if you don't use the correct tools or fail to follow the IFIXIT guide to the letter.

To answer your direct questions:

• Will I have problems with the fan speed I have read about? No
• I've read some say that their fan sped up, others say that it didn't. For the 2012 iMac 21.5" does the fan really speed up? - No, The larger 27" model use a 3.5" drive that uses a custom built-in thermal sensor. Which you need to deal with. The 21.5" models use a standard 2.5" laptop drive
• I don't mind my fan being a bit loud. I just don't my fan breaking because it's at max all the time. If you have a racing fan you have a problem that needs to be fixed. Often its an error in re-assembly
• What are they referring to, CPU fan? Over time Apple has reduced the number of fan units. The 21.5" model only uses One fan
• Will my fan be 100% full power all the time? No
• I don't want to install fan software. Is there another solution to the fan problem if the fan problem really is an issue? The 21.5" models don't have an issue only the 27" models
• Will my new SATA SSD fit perfectly? Yes, the 2.5" SSD is the same size as the 2.5" HD your system currently has