neckband, ruff, neckpiece

Some of the advantages of neckband headphones compared to other types of headphones are that the neckband headphones are more durable and have a firmer fit than the type that only attach to your ears. They are better for runners and other sport players because they stay in place better and have only a single cord on 1 side which makes them less likely to get snagged on something.

You can find the answer on Chabad's website.

Yes, but the neckband and tassels are removed.

It is the neckband or piece of clothing wrapped around a man's neck, primarily a part of formal outfit.