2 Blindfold chess can improve visualization and memorization. 3 Even artistic chess problems can help with calculation, and often use patterns that can be used in your games.
Misguided chess beliefs...your thoughts?

I don’t know what Kotov really meant, but the problem with lower level players is that they want to interpret it as meaning: “I should only look at any line once and regardless of how uncertain I am of my calculation, I should move on and never ever return to that line because it doesn’t help... because that is what a GM says to do, and I want to think like, play like, and become a GM.”

It is my understanding that grandmasters in general don't like to play against computers (especially non-handicap matches). I have heard diverse reasons for this, but I have never quite understood the mentality behind it.
One would think that playing (completely normally, with long time controls, as you would against any human opponent) a game and losing would then help you analyze afterwards why you lost, and what were your mistakes.
To agree with and expound on Bullet6422, blindfold chess is useful to improve visualization, and I've seen it work.
In particular, it helps build one's ability to play out different lines, and reduces one's tendency to forget about pieces placed "away from the action". The first increases tactical effectiveness, the latter decreases the rate of blunders - both very important things.
As for chess problems, if they involve realistic game situations - ones in which an imperfect continuation clearly changes the game result - they can be useful. Mate in _ problems in games which are already trivially won might be of questionable value, but learning to attack and defend most efficiently is essential, as many games involve the winner's attack being just one move faster than the loser's attack.

And bullet chess is detrimental for class players.
Ain't that the truth! AMEN Brother!

For the third point by the OP, regarding the artistic composed problems, I agree with Bullet6422 ... I think chess geometry and comfort with piece movement, square control, schematic goal-oriented thinking, and calculation needs to be learned from as many angles as logically possible, and is essentially what makes someone a stronger player. Even if those types of positions don’t come up in games, the concepts do (such as corralling a king, piece roles/activity/space control, unusual resources by oneself or the opponent, etc.), especially in novel situations for a given player, which come up often.
Arguing about blindfold chess is sort of pointless. I am guesing that probably fewer than 1 out of 10,000 people on this site have the ability to conduct a game of blindfold chess at a reasonable level of play.

Is it possible for a player who would like to play a match and is in both groups for that match on chess.com? It was my belief that they cannot play said match when they have joined both groups. Is this true?

There have been a number of authors who have taken Kotov to task, ignoring his word "strive."
The most common argument is that there are often a few possible variations that are worth exploring for up to several moves and coming to the conclusion that none stands out over the others. At that point it's worth going back and looking more deeply or into more branches.
But basically Kotov was saying to avoid to go back over possibilities you already went over, hoping you'll see something new, when there are other possibilities you haven't checked.
Personally, I'm a weak enough player that if I look at something else and then come back, I DO see new things I missed the first time that a GM would have noticed at once. So, especially in daily games, I do look go back and look for something new to pop out at me.

There have been a number of authors who have taken Kotov to task, ignoring his word "strive."
The most common argument is that there are often a few possible variations that are worth exploring for up to several moves and coming to the conclusion that none stands out over the others. At that point it's worth going back and looking more deeply or into more branches.
But basically Kotov was saying to avoid to go back over possibilities you already went over, hoping you'll see something new, when there are other possibilities you haven't checked.
Personally, I'm a weak enough player that if I look at something else and then come back, I DO see new things I missed the first time that a GM would have noticed at once. So, especially in daily games, I do look go back and look for something new to pop out at me.
Who is Kotov?
He's the author of two EXTREMELY famous books, the first being very famous and the second being about 100 times the level of fame of the first one!
Play Like a Grandmaster
Think Like a Grandmaster

Arguing about blindfold chess is sort of pointless. I am guesing that probably fewer than 1 out of 10,000 people on this site have the ability to conduct a game of blindfold chess at a reasonable level of play.
I aint THAT special *blushes*
... Who is Kotov?
He's the author of two EXTREMELY famous books, the first being very famous and the second being about 100 times the level of fame of the first one!
Play Like a Grandmaster
Think Like a Grandmaster
At one time (~3 decades ago?), I think that those books (along with Train Like a Grandmaster) were indeed famous (as books for stronger chess players), but my impression is that they are now largely forgotten. I do not know how one measures this sort of thing, but, as an indication, one can look at:
https://www.chess.com/article/view/the-best-chess-books-ever
The Think book is mentioned only here and there. Still notable, though.

I wonder what data they interpreted to make the claim that blindfold chess is not worth actively improving in. Intuitively learning blindfold makes sense because when I calculate long lines and play them out over the board I realize that I sometimes miss things I would easily have seen if I could move the pieces on the board to help calculate. If I could move the pieces about and study the positions more accurately in my head then I don’t see how it could do anything but help.
(1) Kotov (1971; 1983) proposed that players should strive at calculating a branch of
the search tree only once. We believe that this advice is likely to lead to disaster in
competition games. As a matter of fact, empirical evidence shows that even top-level
players often re-investigate the same variation (De Groot, 1978). We have more
confidence in the technique of progressively diminishing the thinking time in practice
games, also proposed by Kotov.
(2) We believe that playing blindfold chess is at best useless, and at worst harmful to
one’s development. The ability of playing blindfold comes more as a side effect of
having acquired a well organized and easily accessible knowledge base (Ericsson &
Staszewski, 1989; Saariluoma, 1995). Practicing blindfold as such may be harmful
when it interferes with other types of training.
25/1/05 15 out of 24
(3) Finally, training with artistic chess problems, proposed among others by Chéron
(1942), is probably useless for chess competition. Gruber and Strube (1989) have
shown that there is little transfer between these two variants of chess. According to the
theory espoused here, practicing with chess problems will develop chunks of
knowledge that are unlikely to be of use in competition games, because the conditions
of their application are not met in these games