You can normally leave plants to grow wild but most people will trim them when they get too dense or bushy. Basically you keep them trimmed so the tank looks neat and so the surface isn't covered in plant.
All tetras need to be kept in groups of at least 6 of their own kind. However, it is preferable to keep a minimum of 10 of each type if not more, but it also depends on tank size and if there is enough room for them.
Having 5 black and 1 white skirt tetra should be fine as they will all hang out together so you don’t really need to get more unless you want another white one.
I'm not sure the vallis you have is giant vallis, it looks more like narrow vallis. Giant vallis gets huge and is quite thick, the leaves are about an inch wide.
Your tank water looks a bit cloudy. You should probably do a few partial 30-50% water changes to clear it up. Make sure any new water is free of chlorine and has a similar temperature & PH to the tank.
You have a box filter in the corner of the tank. These should be cleaned about once a month. Take the filter floss/wool and other media out and wash them in a bucket of tank water. When they are clean put them back in the filter. If the filter has black granulated carbon in then that should be replaced each month, or better still just take it out and replace it with a sponge.
When the filter floss gets really dirty only replace half at any time. Then wait at least a couple of weeks before you replace any more.
Filters have good bacteria in them and it is this bacteria that keeps the water clean. If you change too much filter material at any one time, you can get rid of too much good bacteria and end up with water quality problems. By only changing a part of the filter media and then waiting for a few weeks before you change more, you allow the remaining bacteria to colonise the new media and build their numbers back up to a normal level.
