Learn Russian: Он медленный, а я быстрый.

In Russian, the present tense of the verb "to be" is almost never used. Instead of saying "He is slow," you simply say "He slow" (Он медленный). The same rule applies to "I am quick" (я быстрый). This is why you don't see any verb in this sentence at all.

Why do we use the word а here instead of и for "and"?

The word а is a special conjunction used to contrast two things. Because we are comparing "slow" and "quick" as opposites, а is the perfect fit. The word и is used to connect similar things, while а points out a difference. In English, it can translate to either "and" or "but" depending on how strong the contrast is.

Could I use но instead of а here?

You could, but а sounds much more natural for this type of sentence. The word но is a stronger "but" that introduces something unexpected or contradictory. The word а is used for simple, direct comparisons where two subjects are just doing or being different things.

Why do both медленный and быстрый end with -ый?

These words are adjectives, so they must change their endings to match the gender of the person they describe. The -ый ending is the standard masculine ending. This tells us that он (he) is male, and that the speaker, я (I), is also male. If a woman were speaking about a female, the feminine -ая ending would be used: Она медленная, а я быстрая.