An excellent answer! The combat mechanic here is quite similar to Street Fighter V (Light->Medium->Heavy rotation with any move except the final one in the same-button sequence is cancelling into Special/EX/Super/Ultra) plus Mortal Kombat (Breakaway, Button Hold to Block) plus MvC (Pushblock, Counter). For Training, you can try to set a Dummy to repeatedly Attack, Blocking, Breaking, etc. to hone your skill in various situations. The characters with Eclamation Mark on CharacterSelect Screen can be selected, but not all moves are implemented for them. But you can try some moves, like Meiling's Ultra or Lucius' Forward Special, just for interest. About jumping after a move - some moves are jump-cancellable. For example, you can jump immediately after Cr.Heavy Uppercut successfully connects. Cr.Medium always hits a knocked character (it is a feature), Super/Ultra is the only moves those can connect during opponent is Waking Up. The combo system has its own rules and limits, you can learn more in this old video, which is still relevant.
About "long pauses": this is a common feature of all modern Fighting Games. A Framedata. The mostly Damaging moves that you can easily combo off of should have the long startup, so other player can react more easily, and long recovery, so it will be dangerous and punishable, like this flying knee into the Block. Light attacks with low damage and greater scaling are much faster. Risk vs Reward. The more you can get - the more you lose on fail. Don't forget that you can immediately cancel the majority of basic moves into Special, EX or Supers.
It would be absolutely amazing and super helpful if you be so kind and make a recording of your PvP duels. It helps me to understand how a common players are playing, how successful they are in combos, how hard or easy the game is for them. It is mostly important when I'll try to implement various levels of Difficulty, from Casual to Godlike, based on how the players actually play. Also, it will let me see how the game runs in Linux Build, and are there any real lags, framerate drops, etc.