Learn Spanish (Latin America): ¿Tú recuerdas nuestro plan?

Recordar (to remember) is a stem-changing verb. For this group of verbs, the o in the middle of the word changes to ue in the present tense for most subjects (I, you, he, she, they). Because the subject here is tú (you), the o changes, making it recuerdas.

Could I leave out the word tú and just say ¿Recuerdas nuestro plan?

Yes, you can! Because the verb ending -as in recuerdas already tells us exactly who is doing the action (you, informal), the pronoun tú is optional. Including it here just adds a little extra emphasis or makes the sentence sound a bit more conversational.

Why is it nuestro plan and not nuestra plan?

In Spanish, words for "our" (nuestro, nuestra, nuestros, nuestras) have to match the gender and number of the thing being owned, not the people who own it. Even if a group of women has a plan, it is still nuestro plan because the word plan is a masculine, singular noun.

How do I know plan is masculine if it doesn't end in an "o"?