In the first photo, the plant on the right is a Cryptocoryne; a true aquatic. But it is fussy and does not like sudden or significant changes in water chemistry. Try not to move it more than absolutely necessary. Crypts tend to "melt" if the water parameters change, or they are uprooted. Melt means the leaves within a day will melt into mush. But just leave it, the roots almost always live, and new leaves will appear. Crypts frequently do this after being acquired, but they almost always recover within a few days, sometimes longer. They are also good plants for shadier areas.
The left plant is probably the Ophiopogon species. If it is the Fountain plant, Ophiopogon japonicus, it could last a long time, it is quite hardy in aquaria.
Photo two does appear to be an Anubias, if that is how it was labeled; a true aquatic plant. But it should be attached to a piece of rock or wood as it grows with a rhizome that must be above the substrate, and the fine hair roots will attach itself in time to objects like rock or wood. If left buried in the gravel it will probably rot. I like to attach these plants to a small rock or piece of wood, then I can move the rock/wood with the plant around if I want to re-arrange things.
The right plants in the third photo are Dracaena species, like the houseplant, not a true aquatic. These can sometimes last underwater for several weeks but will eventually rot. You can leave it there for now, but as soon as you see any sign of deterioration pull it out so it doesn't rot and foul the water.