Yes, but BE CAREFUL.
Avoid getting scammed. Be extremely wary of door-to-door salesmen or unsolicited phone calls (if that's the way you were approached). Note that they could be lying about the company they work for.
If the representative asks for a utility/phone bill, that bill may contain enough account information for them to switch you to a new service without your consent (in which case, your new bill with that new company will skyrocket, if only for the reason that if they lie to you about one thing, they won't have any other qualm about lying about other things). Or in some other cases, that bill or the information it contains could be used for identity theft.
That being said, assuming you've done your due diligence and you're pretty sure it's not a scam. Even then, I would suggest that you black out your account number, your address, any of your private business info, and your full name from the bill, take a photocopy of that blacked out document, and only provide that photocopy to them (either that, or tear off the private information, but look at both sides of the paper before you hand anything over).
Otherwise, here are my answers to your other questions:
Yes and yes (assuming it's not a scam).
Is it to my advantage?
It could be.
Notwithstanding the already excellent answer from Kevin that I won't repeat here.
The first benefit of providing a copy of your (properly blacked out) bill is a matter of convenience. And the second benefit is discovery. The fact is. This is not a salary negotiation. The stakes are a lot lower to you. And explaining all the options to you may take extra time that you simply do not want to give.
For instance, replacing your old boiler may save you thousands of dollars in energy savings and in government incentives. Or repairing your leaky swimming pool may save you equally as well. But these topics may simply never come up if the competitor doesn't see your bill.
Is this commonplace, accepted practice?
Unfortunately, it's commonplace for both non-scammers and scammers alike.