Tetra Unusual Behaviour

Penguin tetras are prone to some bullying/fin-nipping, from what I've read. While often 6 fish used to be recommended as the bare minimum number for any shoaling species such as these, usually 8-10 is now advised at the very minimum. Generally, the more fish there are, the more aggression is spread out. Check out https://www.seriouslyfish.com/species/thayeria-obliqua  The pointing-upward behaviour is characteristic of these tetra although someone who actually has them may be able to confirm whether that particular angle is normal or extreme and thus perhaps a sign of stress from the bullying.

I have a mix of penguin tetra and black neon tetra, along with marbled hatchets, various corydoras and a BN plec in one of my tanks. All the fish in that tank are south american species.
The angle of the fish shown in the picture is quite a bit more than I've seen with my gang. With mine I've noticed that they only seem to be at an angle when relatively static, but I noticed it more when they were a single species group. I will admit that they are quite a boisterous gang, and I have found that "the more the merrier" is the way forward. I have >10 of each tetra. My current gang seem to mix freely with the black neons, and the mixed group seem to get on quite well.
I'm watching them as I type, and although the mixed group are spread throughout the tank, each penguin tetra appears to have it's own little bit of space, and will chase another fish out of it, but only for a few cm before returning to it's original spot. Weird. 
I guess it is possible that a group of 6 could lead to some being bullied. I'm not great at sexing these fish, but that could also be a factor.
If the fish are more sociable when the lights are out, perhaps some more decor/plants/hiding spots may make them more comfortable when the lights are on.
What other fish does your friend have in the tank? Although penguin tetra are quite active/boisterous, they can be intimidated by more aggressive fish.

As long as everyone is feeding well then I'd guess it was a dominance/territory thing rather than outright bullying. With the numbers of penguin tetras involved it's possible that there is one dominant fish, and the others are just getting out of the way.
With my mix of penguin & black neon tetras it's possible that both species look similar enough to act like one large group of >20 fish, which may spread out any of the sort of behavior you have described.

I have peppered corys in my river tank. It's a group of 8 that I've had for a long time, with 2 being second generation. My 2 older ladies are quite big units now. I have other corys in other tanks, and I enjoy watching them rummage around the substrate and generally pottering around the tanks.

I look forward to hearing about your setup when you;ve finished cycling. 

That practical fishkeeping article is not one I’ve seen before and is a great find