"This is usually shortened to X, Y ⊢ X ∧ Y based on the assumption that everything to the left of the turnstile is assumed to have already been judged to be true. Such a rule can be pronounced as follows: in a context in which you have already judged X and Y to be true you can always conclude that X ∧ Y is true." --> Does this mean that just stating X or just stating Y means that those are true, or does it mean that X is just equal to X? Is it circular, and will the meaning always be this way for inference rules?

[RoboticMind]

The comma doesn't mean that only one is required. Think of it as listing all the things you know to be true (or need to know). If you know X is true and you know Y is true only then can you say that X ∧ Y (read this as X and Y) is true