I am not a campaign manager, but as I have joined dozens of campaign over the last 3 years, I will try to answer to your questions:
1) Why would I need to post my profile link? Isn't it obvious that I'm the user that applies for the campaign? Are there applicants who entered a different link than the one of their profile?
This makes campaign manager job easier. He probably use that link you posted to paste into his excel sheet, to control who is or was in his campaign and received payments. It is much better to save a profile link than just the username (easier to send messages or identify the user, for example)
2) Why do they ask you to wear the avatar and the signature, but they accept applicants whether they wear it or not? Obviously, once they're accepted they'll wear it, but it doesn't seem that this requirement has any point at all.
That depends on the manager. Some managers don't care much about post quality, and will just add the first participants that meet the requirements.
In this case, if the user is already wearing the avatar he has higher chances of being accepted.
There used to be many campaigns like that a few years ago. If a user applied wearing the signature just before the others he was almost guaranteed to be accepted. Even zero merit users with 100% spam history. You can probably still see those campaigns in the bounty altcoin board.
Other campaigns are more focused in posts quality and board participation. In this case, the manager will carefully choose his participants based in his post history/merit/trust/reputation/whatever and he will send a PM to the user, telling he is accepted and asks for him to change his sig/avatar.