What is the difference in usage between these too?
I think it’s like this:
毎年 is for describing the time itself like in “Every year I go to Japan.”.
毎年日本に行きます。
年次 is more of a description for yearly events like “The annual convention takes place in Tokyo”.
年次大会は東京で行っています。
I hope that helps.
Edit: Typo
Edit2: Deleted “の” between 年次 and 大会
年次 can be used as a suffix with numbers to indicate an nth year of something:
ニ年次開講 second year course
Or prenominally:
年次会議 annual conference
毎年 can be used as a noun on its own.
It’s a time word kind of like 今日 in my experience in that it’s often thrown in at the beginning of a sentence, or halfway through, as a time marker without accompanying connectors.
毎年 日本に行く
多くのアメリカ人が毎年日本を訪れる
Edit: Like @MeepleKun notes, you can also use の for the prenominal usage of 年次 but it’s often omitted IME.
Ah, you’re right. I’ll correct it. Thanks.
Nah you’re fine. It’s not wrong or anything and I have seen it used like that.
It’s just that 年次 as an on-on reading carries a bit more prestige, if you will, so when it’s used it’s usually stuck to a noun. Kind of like the difference between “annual” and “yearly”. One sounds a bit more posh. 
Thank you!
I’m baffled by this. How does this relate to the definition we are taught (“annual”)? Or is it a different definition. And can’t you just drop the 次 like how we write 二年生?
I completely get this. I am not fond of words that use Kun’yomi readings myself.
I’d say it’s just a different definition. It’s listed separately in monolingual dictionaries anyway. You need to remember that 次 as a kanji also means ‘time’, like ‘once’, ‘twice’ and so on. In the ‘1st year’, ‘2nd year’ etc definition, the 次 in 年次 is just a way of counting the years. As one answer on iTalki puts it, it’s the same thing as 二年目 and so on.
You can substitute something else for 次 if that’s what you mean, yes. 二年生 would specifically mean ‘second-year student’ though, I think.
It’s the second definition on Jisho:
I may have lifted an example or two from there. 

I haven’t seen this personally, but I imagine you could say 二年次学生 if you wanted to be loquacious about it. 
OP are you aware of these threads??
You don’t have to create a new topic for every language question you might have.
Ermahgerd. My bad y’all, sorry. I knew about the grammar one, but didn’t want to spam it with vocab questions.
The road to hell…
Thanks for pointing it out!