Learn Spanish (Spain): Quizás te guste el nuevo corte. - Maybe you will like the new haircut.

This ties into your current lesson! The word quizás (maybe) introduces doubt. When you use adverbs of probability like quizás, tal vez, or probablemente, you use the subjunctive (guste) to show you are less certain. If you felt very confident that they would like it, you could actually use the indicative here: Quizás te gusta el nuevo corte.

Since the English translation says 'you will like', why isn't the verb conjugated in the 'you' form?

This is a classic quirk of the verb gustar. In Spanish, you don't say 'you like the haircut'; you say 'the haircut is pleasing to you'. The grammatical subject of the sentence is actually el nuevo corte (a singular 'it'), which is why the verb is conjugated in the third-person singular (guste). The te just tells us who is being pleased.

Does the 's' at the end of quizás change the meaning compared to just saying quizá?

Not at all! Quizá and quizás are completely interchangeable and mean exactly the same thing. You will often hear quizás used when the next word starts with a vowel to make it flow better, but as you can see here before the consonant t, it is perfectly fine to use it anywhere else too.

Does corte always refer to hair?