Learn Finnish: Muistatko sinä?

The suffix -ko is a question particle. It turns a regular statement into a yes/no question. Since muistat means "you remember", adding -ko turns it into "Do you remember?".

Do I always have to use the word sinä here?

No, you can just say Muistatko? and it means the exact same thing. The -t at the end of the verb already tells us "you" are doing the action, so the pronoun sinä is optional. Including it just adds a little emphasis, like "Do you remember?".

Since this lesson is about negation, how would I say "You don't remember"?

You would use the negative verb et (you don't) and the stem of the main verb. To get the stem of a Type 1 verb, take the "you" form (muistat) and remove the -t, leaving muista. So, "You don't remember" is sinä et muista.

Does the verb muistaa change its stem to a "weak grade" when we make it negative?

No. Consonant gradation only affects specific consonants (like k, p, and t) in the middle of a word. The consonant cluster -st- in muistaa does not change, so the stem stays exactly the same in both the positive (muistat) and the negative (et muista).