Gratiola virginiana, maybe? WW Here is a link that might be useful: Gratiola virginiana

It is trailing arbutus, Epigaea repens. It is actually a shrub, although it appears to be a vine.

It is hard to tell the scale of the picture; in other words, I can't tell how tall the plant is, but it looks a lot like a sedge in the genus Cyperus. These are usually called Nutsedges for the nut-like nodules on the roots. They are native, but a weed in gardens. There are several species, I think.

You can use any plant you like (and have access to). Invasive is only an issue if you start spreading the plants outside; so, don't do that! I don't see the holes for plants. If the plants go in the water, then they will have to like water, but if they are somehow outside the water then any thing will do.