[mothered]

would you recommend I don't be greedy and just go for the coat on it's own?

Obviously claiming just the one Item attracts less attention.

That being said, the hoodie Is a low value Item, so I don't believe It will Impact your claim.
Ultimately It's your choice.

Also, if I use student discount on my order would that have any potential impact on my SE? (would be my friends code, I'm not a student)

That's fine - It's purely used for buying purposes, so there'd be no reason to affect your SE.