I agree, it's temperate hornwort, Ceratophyllum demersum. The other plant in the first pic is waterweed, Elodea canadensis. The other plant in the second and third pics is curly pondweed, Potamogeton crispus. The algae you describe could be a Cladophora species, but don't take my word for it.
Unfortunately, these are the crispest pictures my camera would do. I took about ten shots with different settings and those were the best. I might move them into a different container and try again later. For now, the guesses I got seem right on.
The elodea and hornwort are both floating plants for sure, but I planted them in the gravel so my wife would tolerate this living vase on our desk. I'm amazed she hasn't thrown a fit about the hydra. I suspect that the gravel is open enough that the stem below the substrate won't rot much. Also, my tapeworm seems to wrap himself around the base of the plants and I'd hate to kill him be taking that away without understanding how he survives. I'm suspecting more and more that he's not a tapeworm but some sort of aquatic flatworm. If he reproduces I'll be so stoked...