Why are lower leaves yellowing and then wilting? Is this normal for tomatoes?

I'm going to apply fertilizer but how long do you think it will take to recover?

Agreed, the plant will focus nitrogen reserves on the newest growth, this the lower leaves will begin to yellow. The lower leaves may not recover, but being that it is a Tomato, you can prune those off. Feed your plant a good all purpose plant food per the instructions on the bag and it will stop the yellowing.

I pruned them and I'll now fertilize them.

I'm now seeing fungus gnats and more leaves wilting. Could that be a problem as well?

Your soil may be a bit too moist of you are seeing fungus gnats. I usually keep the bottom foot or so of my mature plants completely pruned clean, and then continue up the plant leaving only the branch directly under the lowest fruit set. A $15 moisture/pH/light meter may help with troubleshooting

I actually have one of those meters and I've been trying to not water the plants until it measures moisture below a five on the meter. I just pruned the wilted leaves off so it looks a little more trimmed now. I've been applying AzaMax as a foliar spray as well.

Sounds like you are on the right track

It seems that adding fertilizer, using plant food, watering less and pruning the bad leaves worked! Here's the plant now!

Excellent! Glad to hear it is recovering