Would you be able to add numbers next to the plants in the first (complete tank) photo? This would make it easier to provide names for this and that plant.
The plants in the shrimp tank are easy to distinguish. Left to right they are (I think
) Sagittaria, Bacopa, the single stem is Egeria (or Elodea), the low plant in the back is i think Anubias (as is the low plant at right front), then Bacopa again, then the stem plant we tried to ID in another thread a few weeks back and I've forgotten what was decided.
To the question on trimming, this is up to you based upon how you want the plants to grow. Stem plants will simply grow longer stems toward the light source. If you want to keep them below the surface, pull up the clump when needed, cut off the top portions (length is up to you provided there are several nodes, nodes being the point from which the leaves grow on the stem) and replant the top cut portions. Discard the lower portions. With some stem plants, you can leave them and cut off the top portions the same and replant those. The bottom portions may sprout new shoots. This depends upon species. And whether you want more of the plant. Usually it is better to pull the stems p and cut and replant the better-looking tops.
If you allow them to continue growing at the surface, they will sometimes grow along the surface, sometimes up above; depends upon the species. But in either case, the lower leaves usually rot off due to less light and the plant putting most of its energy into the growing tips.