I applied for a job. (Sense of 'for'=asked for something in writing)
I applied for my friend. (Sense of 'for'=on behalf of)
Are those sentence correct?
Can I use 'for' in this way, because already a fixed preposition is there?
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Sign up to join this communityYes, you can "apply for someone" meaning "on their behalf". It just implies that the thing you're applying for is elided.
— Congratulations, honey! You got the waiter job!
— Huh? I didn't even apply for it.
— Oh, I applied for you. I figured it was about time you started working during the summers.
— Mo-om!!
By the way, the sense you supply for "for" in the first case doesn't make sense. It has nothing to do with writing. If you want to supply a synonym for that "for", it would be "to request".