Hi and
to garden.org!
Your plant is not a Palm Tree but rather
Dragon Tree (Dracaena reflexa var. angustifolia) and if you click that blue link it will take you to our database entry where you will find growing information and lots of member photos.
Does your pot has drainage holes in the bottom? Good drainage is extremely important. The soil your plant is in appears to be quite dense and is likely holding way too much water. In my experience, a light and airy soil is a better choice, one with lots of perlite added to create air pockets for oxygen. As for the depth your tree is planted, I always try to pot plants at the same depth they were originally growing in their pots but the current depth of your tree shouldn't cause any harm. I think one I planted in my yard has roots above the soil line like that. The main thing is that the soil you are using may be way too heavy, which can cause lack of proper aeration and drainage. If it were mine, I'd definitely repot and mix in lots of extra perlite (and orchid bark mix) to create a chunky, airy substrate that will allow for more oxygen in the soil.
I'm in zone 10a Florida and I've been growing this plant for many years; I have quite a few planted in my yard as well as a few container plants on my pool deck and on a screened porch.