It really needs to be either 2 or 4 clubs getting promoted. The problem with promoting 3 clubs with no relegation is you'd then have a league with an odd number of clubs, a PITA from a fixture planning point of view with the additional big downside that one club would finish it's season before all the others. I agree the season probably won't start earlier than September and I think the PL and FA would want the 2020/21 season to end in May.
IMO it's highly likely the League cup will be suspended for the year to help with fixture congestion but with 4 extra PL games plus the usual European matches that still won't be enough. One option could be to give clubs still in Europe after Christmas the option of either withdrawing from the FA cup entirely or fielding a fully second string squad, FA cup games could then be scheduled on the same days as European matches.
I can't see that it would be too much of a problem. There are only 23 clubs in League 1 this season due to the Bury situation. There have been odd numbers in the top tier before, whenever they have changed the number of clubs. The old first division used to have 22, the EPL currently has 20, but at one point I recollect that there were only 18. Each time they adjust the numbers by changing the number by one, although obviously this would have to cascade down through the leagues.
If there are promotions but no relegations this year, then the Premier League will have 23 clubs instead of 20, but who knows what the European situation will be? We could be in a position where it is safe to play in England, but not necessarily in other countries, which could mean the Champions and Europa leagues not being played, or, as has been suggested earlier, EPL teams could be excused from entering the League Cup. (Wouldn't a Football League only cup be great)? The EPL can then revert to 20 if it wants to by an extra relegation for the next three seasons, or maybe including the fourth from bottom team in the play offs.
By good fortune the numbers in League One will increase back up to 24 by virtue of the fact that four teams are as a matter of course promoted from League Two to League One. The only problem will be in League Two, where they will lose the top four (or top three plus play off winners) but will only have two promotions from the conference so will be reduced to 22.....unless there are two extra promotions from the National League.
As an aside, last night I was watching a YouTube video about what could happen to the current season, and the idiot who made the video seemed to think that if there were no relegations there would be extra games in each division!!! I was hoping that he might explain where all these extra teams would come from but he didn't.