Instead of that gravel you can use sand, or soil, (if you want a planted tank). You'd want to get something either small enough that it can pass through their system without causing harm if accidentally ingested, or something to large for them to swallow in the first place. I personally use large river rocks that are about the size of the newts. I like this choice of substrate because it looks good and natural, poses no dangers to the newts, and are the easiest things to clean. I just vaccum between the spaces, and if the need arises, it's easy to move then ones you need to without affecting the rest of the aquascape.
Good job with buying the plants and increasing the water level! You should definitely get more when you can, and your ten gallon set up should literally have about 20X that amount of plant life. If possible find varying species as it will give your tank a interesting look. It's also important to find a tall sturdy plant that they can use to hang out in near the surface. Cabomba and Sprites are what I use in my tank but I'm sure you can find others.
In your current container I would remove all the gravel as it will trap waste and use up water volume. Go bare bottomed for now, and as it will allow you to see the poops, be very diligent and clean them all up as soon as you see them to keep your water clean (a difficult task in such a small unfiltered volume). The newt will have more water to swim in but still be able to access his rock. Change about a 3rd of the water daily. Soon he should be more and more comfortable in the water. After some time you should increase the water volume as much as possible. Maybe double what you already have or even triple it. Then find something you can use as a floating island. Next put in something that slopes from the bottom of the container to the top that the newt can use to easily access the surface, be it a plate or tile or some plastic mesh( a piece of driftwood would do great too, but research first about sanitizing it for tank use.). Try to avoid using the large rocks since they eat up a lot of water volume, and stacking them might pose a risk to the newt if they fall.
For earthworms, I keep mine in my apartment as well. You just need a small bin, about 2ft by 2f with a one foot depth is adequate. Nothing fancy, any plastic bin will do. Fill it up with soil, cardboard, dead leaves, and drill holes in the bottom and sides ( small enough to drain water but too small for worms to escape). Make sure to keep this mixture moist, but never soggy. Put the worms in here and feed them vegetable scraps every few days. They should be fine as long as it doesn't freeze
