Is a motel close by

There are a few close to Arlington National Cemetery. The Sheraton Hotel is two miles away from the cemetery. There is a less expensive hotel close by, Days Inn, 1.5 miles away from the cemetery that will put you close to the Iwo Jima Memorial entrance of Arlington National Cemetery. The other hotels are in Arlington, Crystal City, and Washington DC. Another option is to try one of the Air BnB's in the area. They are friendly, within your price range, and you will have a better chance to get close to the things that you want to see.

Yes there quiet few of them

There's a couple not far from there

Yes