Learn Russian: Сколько стоит чай?

No, стоит is a regular present-tense verb meaning costs (from the infinitive стоить). Because you are currently learning commands, you might be thinking of the imperative стой or стойте, which means Stop! or Stand! (from a different verb).

I've seen a similar word that means stands. How do I tell them apart?

That is a very common mix-up! The verb for costs is stressed on the first syllable: стóит. The verb for stands is stressed on the last syllable: стои́т. In everyday writing without stress marks, you can always tell them apart by the context of the sentence.

Why doesn't сколько change чай into the genitive case?

Great observation! Usually, сколько (how much/how many) forces the following noun into the genitive case, like сколько чая, which means how much tea (as a quantity). But here, сколько describes the verb стоит (how much does it cost?). Чай is the subject of the sentence, so it stays in its dictionary form (the nominative case).

Can I change the word order and ask Сколько чай стоит?

Yes, Russian word order is very flexible and you will be perfectly understood. However, putting the verb before the item (Сколько стоит...) is the standard, most natural phrasing you will hear when asking for prices in shops and cafes.