yes it really does matter what game mode you are playing, in team games both sides are supported so its easier to develop counters to any problem unit,
Assuming your mate has your flank covered and actually wants to play a 2v2 match as opposed to a 2x1v1 one, you are correct.
However, if that is not the case you are stuck having to counter all units by yourself on an area that is roughly the size of a smaller 1v1 map where pretty much all sets of 1v1 circumstances apply.
1v1 is the test base for any problems and their answers in coh 2, its a reaction unit, if the luchs gets attacked by a counter it moves to the other side and harasses
And that is exactly the point of a deterrent unit. You want to force constant retreats and repairs because those sorts of things just buy you time to inflict as much damage as possible on volks/pios and not bleed your MP, leading you to tech up to hard counters. Furthermore, harassing situations on the opposite flank open up opportunities for ambushing with combined arms: mines, demos, PTRS penals, guards, AT nades, etc.
it works much like the T70 but comes out a lot earlier, it can even harass the base until hard counters arrive, PTRS is a double edged sword on penals, there is still a blob of OKW terminators to deal with if you manage to counter the luchs, penals are expensive and will be outnumbered, so downgrading their ability to fight inf for a second rate and almost useless at ability is a last resort.
This doesn't sound right. If you are referring to luchs rush strat, then there is no way he can have "blob of OKW terminators" (unless you bled hard and they gained vet quickly). The earliest luchs can come at 6 min mark where he can only have 3 questionably healed volks, a sturm pio and a support weapon while soviet army will consist of an engineer, 3 penals, DSHK/Guards or any similar variation like that. If the opponent blobs 3 volks hard, then get a DSHK and PTRS on a single guard squad. Have DSHK support one non PTRS guard squad when dealing with the blob while the rest of the units deal with harassing luchs on the flank.
On the flip side, if the opponent spreads units across the map and uses luchs to support a push on particular flank, call in guards and keep them in the middle so they can support any flank in a reasonably timely manner. In the meantime, inflict as much damage on volks and other infantry through superior positioning. Penals will beat volks in green cover on any range and on longer ranges outside of cover.
I understand this is much easier said than done, but at the end of the day you need to outplay your opponent. Sure, you are going to get raped by luchs from time to time when things go south, especially vs a well rounded opponent, but at least that gives you the ability to analyze luchs usage paterns and react better in the next games.