Learn French: Restes-y encore un peu. - Stay there a little longer.

You are absolutely right! Normally, the tu command form for regular -er verbs drops the "s" (for example, Reste ici). However, when the command is immediately followed by the pronouns y or en, French adds the "s" back in to prevent two vowel sounds from clashing.

Do I actually pronounce the "s" in Restes-y?

Yes, you do! The whole reason the "s" was added back is to create a liaison (a linked sound). You pronounce it like a "z" connecting the verb directly to the pronoun, sounding roughly like "rest-zee".

Why is there a hyphen between the verb and y?

In affirmative commands—when you are telling someone to do something, rather than telling them not to—French attaches object pronouns directly to the end of the verb using a hyphen. If this were a negative command, the pronoun would go back in front of the verb with no hyphen: N'y reste pas.

I learned that encore means "again" or "still." Why is it translated as "longer" here?

Encore is a highly versatile word. While it frequently means "again" or "still," when it is paired with a quantity or a duration like un peu (a little), it takes on the meaning of "more" or "longer." So encore un peu translates naturally as "a little longer" or "a bit more."