Yes, check your tap water, though as ammonia is decreasing with each water change it is likely from the tank cycling. But still wise to know.
Yes, add plants. They will quicken the cycle and if you have enough prevent any problems.
As for the substrate, 2-3 inches is normally good depth, but the size of the gravel is important. If it is too large, not only will plant roots have trouble, but the biology will too. Waste from the fish needs to be able to settle in the substrate so bacteria can break it down. If the substrate is too large a particle size, too much chunky food can get trapped and it is difficult for bacteria to break this down. With smaller grain gravel, the waste gets broken down more on the surface--fish eating it, snails etc. So the bacteria can more easily handle it.
If you are going to add smaller gravel under what you have, it would be prudent to consider replacing the substrate completely. Depending what it is, this can be better. The substrate is the most difficult part of setting up a new tank, because once set up the substrate is the most difficult to change, so make sure you have what you want--and what will work best--before you go further.