Erinbirdsong, welcome--you and Preston--to Tropical Fish Keeping forum.
On your first question about suitable live plant species, I will mention a few that are easy plants; the names will shade meaning they are in our profiles with photos and care info. Easiest of all and also the most useful are floating plants. Water Sprite is top choice. Some stem plants grow well floating too, as Wisteria someone mentioned earlier, Brazilian Pennywort [works very well], and Hornwort [not in our profiles but a commonly-available stem plant]. For "planted" plants, chain sword or pygmy chain sword is almost indestructible. Java Fern and Anubias can be attached to wood/rock/decor.
Now to the fish issue. It is true there are differing opinions on many aspects of this hobby. The trick is to sort out those who know from those who don't; the source of the info is important. Advice from fish store staff is often, sadly, less than accurate. I do not believe these people are deliberating misleading, but they simply do not know. Most stores do not have any form of training beyond doing what the other staff are doing. If one has a local fish store run and staffed by hobbyists, that is a real advantage. The data in our profiles is accurate because it is what all who know these fish will advocate. I wrote most of the freshwater profiles, and I used the acknowledged authorities throughout.
All tetra, and many other fish too, are shoaling fish. That means, they live in large groups of hundreds, and being in a group is an essential part of the fish's requirements. Most suggest six as the minimum number for a tetra species, but more is always better. However, tank space has to be considered, and as someone mentioned, a 10g is very limited space. Some of these fish should be in a larger (length) tank (a 15g or 20g) minimum, and all the tetra need a group of more than six.
Now, the reasons. Shoaling fish have a need for numbers as security; the more there are, the safer they will be. And that means less stress, and stress is the main cause of all fish disease. Second, there may be a hierarchy within the group, natural to the fish; interactions between males, a pecking order, etc is a part of the fish's needs. When denied this, fish can react in various ways, but the most common is aggression. The fish is simply frustrated at not being in an environment that nature programmed into it, and it lashes out the only way it can. Other times, the opposite may occur; the fish becomes withdrawn. In both cases, stress again results, leading to health problems. Some of these cannot be seen until it is too late; when fish die earlier than their normal lifespan, it is almost always due to some facet of stress caused by an inappropriate environment.
At the moment, the fish are in a new environment and they are still adjusting. As time goes on, things will change, it is guaranteed. The fish will either become aggressive, or the opposite and weaken. If it is possible, returning some of the fish is the best solution, assuming another larger tank is not feasible. As for what to return, the "skirt" tetra are known fin nippers and the lack of a group and in so small (to them) a space is going to bring this out eventually. The Red Eye is similarly inclined. The Glofish is a form of the Zebra Danio and also shoaling.
And corys are highly social fish, and must have a group. Sand would be better, but I won't get into the changing of substrates now.
I hope this is of some help in understanding the issues.