Learn Turkish: Tüm öğrenciler geldi.

Tüm is an adjective meaning 'all', so it simply goes in front of the noun: tüm öğrenciler (all students). Hepsi is a pronoun meaning 'all of them'. To use hepsi, you would need a possessive phrase: öğrencilerin hepsi (literally 'the students' all of them'). This sentence shows the simpler adjective way to say it!

I learned that nouns stay singular after quantity words. Why is there a plural suffix on öğrenciler?

You are remembering a great rule! It is true that after numbers (iki öğrenci) and quantity words like birkaç (a few) or çok (a lot), the noun stays singular. However, tüm (all) and bütün (whole/all) are exceptions. When talking about multiple countable things, they require the plural suffix: tüm öğrenciler.

Why is the verb geldi (came) singular if there are multiple students? Shouldn't it be geldiler?

In Turkish, if the plural subject is human (like öğrenciler), making the verb plural is optional. Both Tüm öğrenciler geldi and Tüm öğrenciler geldiler are perfectly correct. If the subject were an animal or an object, the verb would have to stay singular.

Could I use bütün instead of tüm in this sentence?