Improving your chess without access to OTB tournaments Due to the Coronavirus, all chess tournaments and activities have been canceled in my area. At the same time, I've got a lot of time on my hands right now and would like to work on my chess. I have got access to a lot of training material, which includes a vast library of chess books on tactics, openings, endgames, and positional play. I'm rated about 2050 FIDE. Here are my main questions:


What do you think is the best time control to play online to improve? I have found that rapid games (10 minutes each) don't leave a lasting impression, meaning I quickly forget what happened and probably also don't learn much from it. 
Have you tried improving mainly via online chess and can share your experiences? If not, do you know anyone who has done that?
Should I set up a real board while playing online to recreate the OTB experience?
How much training per day do you recommend? I plan on working between 1-2h every day on chess and playing long games regularly.
Overall, I like your plan. Addressing them, not in order though, and adding some thoughts along the way:

How much training per day do you recommend? I plan on working between
1-2h every day on chess and playing long games regularly.

Let's face it, the more time, the better in terms of really getting better. Spending two hours per day is a lot for a non-professional, and is a great commitment.

Should I set up a real board while playing online to recreate the OTB
experience?

I love this idea because I think that playing online, even at slower controls, leads to the click-first-then-think mentality. I see this mentality a lot with the chess.com daily puzzle and many weak players saying &quot;easy&quot; when they &quot;solve&quot; a super-hard study. They got through it, but they clicked until the puzzle accepted the move, rather than truly seeing the solution and then clicking it in.

Have you tried improving mainly via online chess and can share your
experiences? If not, do you know anyone who has done that?
What do you think is the best time control to play online to improve?

I really cannot say that I have because most of my improvement took place long before the advent of the Internet, but I did use an old standby: Face-to-face training games with a friend, who was rated similarly at the time. I do not see why you cannot find a player online, who is interested in doing this with you.
As part of this, I want suggest that you use a long time control (like 40/2 60/1) so you have time to really train your thought process. You should even use notes regarding things that you want to make sure you want to address in your thought-process training. I am not talking about notes regarding specific moves, but notes about the things you want to train as part of your practice.
For example, as I have been getting back into OTB play, here is a list of things that I want to look for. My list might help you, but you should add your own items to it.

Pay more attention to leads in development, and open the position when I am ahead in development. Pay attention to tempi, and not just in the opening.
Every few moves, or after a major change, look at every move for both sides.
Think more about the pluses and minuses of each piece, and how well they are, or are not, placed. What squares do they deny the opponent’s pieces?
What square do I want for my piece, and how do I conquer it?
When beginning to calculate, ask “what is hanging?”  Also ask if there are any double attacks or pieces that can be drawn into a double attack by a sac.
When I find a good move, just look at the other moves to make sure there is not a better one.
Look for pieces in a line so a pin might win.
When calculating a tactical sequence, make sure that you properly evaluate the final position, and that there is no extra counterplay left. Before making the final move, think about all his possible moves as in number one above.
Think more about going after the opponent’s King.
Think more about how to gain space by pushing pawns on either flank, that is play on both sides of the board, if possible.
Ask what is my worst piece, and where is its best square, and move it there.
Ask what pieces should I trade? What is my weak piece and what is his strong piece?
When lacking space, think more about trading.
Ask myself, “what is his moving trying to accomplish?” and “what can he do after I move? (look at all his possible moves as in the mate-in-two problems)” “What is his plan if I were he?”
What structure am I playing for?
When accepting or changing a structure, see if the pieces are misplaced on either side with regards to helping the structure, and enforcing or containing pawn breaks.
When the opponent’s pieces are misplaced, open the position.
Look more at opening the position when I have the two Bs.
In conjunction with asking “where is my pawn break?”, look more at pushing my pawn majorities when I have them.
Think more about dynamic play when I have static deficiencies, or am worse.
Think more about resulting endgames.