How often should I refresh the sealant in tubeless tires?
At minimum, you should replace the sealant every 6 months or so.  As you have found, a good tubeless setup will stay inflated well beyond that time, as the latex in the sealant has already sealed any small holes.  However, the sealant does dry over time, so the systems ability to self-repair when you run over a thorn or sharp rock is greatly reduced.

There is no need to clean and remove the old sealant.  However, some brands tend to leave clumps that you can pick out.

If you're valve cores are removable, the easiest way to add sealant is through the valve.  Otherwise, you'll have to break the tire bead off the rim (just a small section) to add sealant.  This can sometimes take a few tries to get sealed again (helpful to have a compressor or large CO2 cartridge to "slam" the tire into the rim).