Concerning the mystery tetra. I think this is Hyphessobrycon erythrostigma, Bleeding Heart, rather than the "gold" form of Pristella maxillaris. I have never maintained the latter (i.e., the gold form, I do have the natural) but from my comparison of photos online--bearing in mind my friend Heiko Bleher's advice to me that online photos of fish are always suspect
--the fin colouration and markings are not compatible. The poor fish in the photos is certainly washed out, but that is frequently the case with this species, it rarely looks good in the poor conditions of a store tank.
I would return it for another Pristella. This species, the BH, needs a group as it may fin nip if stressed, and this fish will be stressed on its own. This is not a species to maintain without a good group. I have a small group of them (lost a couple due to an internal protozoan a month or so ago, will be getting more) and they are always close, and with the very similar and very closely-related H. bentosi. They are close cousins so this works out well, but notwithstanding their friendship together I will be adding to the BH.
To the behaviour in the video, that is normal. I suspect the black-spot fish doing the chasing is a male, I spotted a couple of male displays during the sequence. However, the black mark is disturbing. I have seen this, or something very much the same, a couple of times on a characin, and the fish slowly weakened until death. I say slowly because it was weeks and even months. I've no idea what it is, but it did not seem to spread to other fish, and the fish itself continued relatively normal, so I left it. I'm no expert on disease issues, so this is just my experience that may or may not be pertinent to what is on this Pristella maxillaris.
And last on the gourami, i agree, that is not a Dwarf, but a Blue Gurami. I would return it, this too is risky. Both from the ppoint of view of the gourami, and the characins that may well nip it.