How does a university legally investigate and prove potential plagiarism cases?

You have already made the matter public by posting here.

The answer above is a good one. Your friend can't just take the trademark and use it for profit. Investigate what 'fan' use is available. While...

You could try again. But look for "buttons" that ask about previous applications and fill out accurately. If the rejection was over a formality...

Would it be "reverse passing off" to purchase a large quantity of human soap and re-bottle it for animal grooming use?

There are likely to be too many other variables in the real world for an answer here to apply to all possible scenarios. The best we can say is...

Can I get compensation for an idea/concept I had years ago that is now being used daily?

The answer above is a good one. You can't enforce rights in an idea. If you register your copyright you would still have to prove there.was...

Is it wise for a company to talk to the press before starting a law suit?

Don't do it until you consult with a lawyer. Among potential dangers are counterclaims for disparagement and if you are wrong about who has...

Artwork is copyrighted automatically once it is finished. You can't enforce the copyright until it is registered. But copyright does not protect...

I'm thinking of trademarking a slogan, it was used by someone else but it looks like it's not registered?

That's pretty much the opposite of what is permitted under trademark law. You'd better hire a lawyer to learn about the consequences of fraud.

There are too many variables. A school name that is the name of the town would be different than a very famous institution with famous sports...

Can I resell items from a consignment store on another reselling website and make a profit by marking up the items?

The first sale doctrine permits a purchaser to resell physical items that have been sold under authorization of the manufacturer. Exhaustion lets...