Welcome to The Helpful Gardener. Don't fret about long posts or lots of questions. Let's see if I can answer them for you.
How often should I repot?
This can be a difficult question to answer if you are looking for a time line. Repot when necessary, which would be when it starts to become rootbound. Things that will effect how often are the type of pot it grows in (clay breathes and roots tend to grow a bit faster as they get more O2), the smaller the plant the more often it seems to need repotting as it often grows faster, fertilizing on a regular basis can cause more frequent repotting, the plant's growth habit can also determine this. For a tree that is 5' or taller and healthy, once every 1 to 2 years should do it. If you need info on how to do this just lmk.
What sort of soil mix should I use?
I prefer a good organic potting mix that doesn't contain any synthetic fertilizers. Most mixes don't have enough perlite (to add grit for drainage) in them, so I purchase a bag of perlite and mix it into the potting mix. It helps with drainage. DO NOT breathe the dust when adding it to the mix. Here's what a good ratio should look like.
Would it be a bad idea to include some slow release fertilizer?
Slow release fertilizers are synthetic and I prefer organic ones. They only last about 3 months anyway and you'd still need to fertilize from time to time. I like fish emulsion or fish emulsion mixed with sea weed. The fish emulsion has an unpleasant odor but it dissipates after mixing with water. Synthetics also leave behind residual salts (more on this later) and can cause a flush of lush growth that attracts insect pests, even in the house.
If I'm supposed to repot more frequently than once every couple of years, I'm overdue -- should I wait until it looks a little better, or go ahead and repot now?
If it needs repotting it won't look better by waiting. I'd say do it now.
How much water does it need, and how often?
This also depends on the type of pot (clay pots allow air penetration and dry out more quickly then plastic, glazed ceramic or fiberglass), how much sun hits the pot and dries it, how many roots are in the pot to drink up the water, etc. Water needs should be determined by the plant's preference and can be determined by sticking your finger into the soil. With my ficus I water when the top 2" of soil are dry - up to the second knuckle of your finger. After a while you'll know by looking at the soil.
Even between long breaks in watering (over a week and a half) the bottom of the trunk looks damp. I know no one here would water it to a "soggy" point, but perhaps they are watering it frequently in small quantities...
Could it be possible that water remains in the saucer? If not, then your suspicions could be correct that there is frequent and shallow watering going on, keeping the top of the soil moist.
There are roots right above where the soil meets the trunk - those seem to have grown recently - should I cover those with soil, or leave them bare?
Leave those alone. It's the nature of the tree to have surface roots and covering them could harm the tree.
Is salt accumulating in my soil? I see a little stuff crusting a tad on top -- is that salt, or a mineral, fungus, something else? Should I do something about that?
It could be salt accumulation you are seeing, but since you mention that the trunk appears damp at the soil, it could be fungal. Remove the soil with the white stuff and repot. You could also flush the soil to flush out the salts. You can do this a couple of days before repotting. If the pot is large then put it in the bathtub and let the water run through for a few minutes to flush out the salts.
Can I root a cutting by air layering?
Yes, but you don't say which Ficus you have and some are easier to air layer then others. Do you know which one you have?