Sure, I can explain.
Rhetoric doesn't level up, but you can find level II and III critique cards just by playing normally. Depending on your choices, you may already have some! Otherwise, consider pursuing some optional objectives, since that's a consistent way of finding new cards. That being said, level I critique cards are less expensive than the higher-level variants, so they tend to maintain a certain usefulness even with the higher-level variants available to you.
The Enthymeme is a means of passively accruing premises. Its "pitch" (or color) determines what kind of premises you gain at the start of your turn, and its tier (or level) determines how many you get (up to +3). The pitch also somewhat increases the weights of arguments that use premises of the same color/mode. The Enthymeme is symmetrical, so its effects apply to both sides equally.
Debate Pace simply refers to how many actions-per-turn each side can take. At a pace of one (the default), you can only perform one "action" (e.g. playing a card, resonating an argument) before your turn ends. At two, you can perform two actions, and so on and so forth until the cap of 3 actions-per-turn. Debate Pace will reset to default after a certain number of turns since it was increased pass.
Proposal slots determine how many proposal cards (e.g. shields, reflectors, status effects) you can have active at the same time. Run out of proposal slots, and when you try to play a new proposal, you'll have to replace one of your old proposals, thereby losing its effect. You can increase your number of proposal slots by simply progressing the story, or by using certain pieces of equipment.