I would like to know the ID of the plants in Picture 1 and Picture 2, and if they are invasive and require removal, or desirable.

Thank you!

2nd pic the stuff with the long leaves floating on top is American Pondweed. Very nice to have. I have quite a bit of it in my pond.
It's a rooted plant that provides very good habitat for YOY fish, grass shrimp, insect nymphs, etc. In my pond it doesn't grow in water deeper than 4'.

The slimy, bubbly floating goo is FA. Not so nice. Cutrine+ and a rock rake will help to control that stuff.

Not sure about 1st pic.

First pic looks like Water Primrose...

https://nature.mdc.mo.gov/discover-nature/field-guide/water-primrose

Amercian Pondweed (Like Augie said)...

https://nature.mdc.mo.gov/discover-nature/field-guide/pondweeds

Filamentaous Algae (FA)...

https://nature.mdc.mo.gov/discover-nature/field-guide/filamentous-green-algae-pond-scum

Nobody wants very much of the FA, but the other two are welcome in most ponds. If it gets beyond your desires, it can be killed back (mechanical removal or herbicides), but it's uncommon for anyone to want or need to eradicate them from the BOW. I am trying to esatblish both in my young pond.

Thank you for the replies. That is exactly what I needed. Nice to know I have some desirable plants beginning to grow. I will now add a few more that I purchased...hybrid lilies, etc.

The water primrose in the first picture is one of the favored covers for grass shrimp here. Find a location where submerged coontail meets floating water primrose and you have their absolute favorite place to be...