Is there a device that gives you access to the Internet that you can buy in your store and plug in your house ?

No

A pay as u go air card will work but it's cheaper to get one under contract. Or get comcast or atandt

Must have an Internet provider unless you're extra savvy with your electronics. If you're able to find a good deal with AT&T, etc., grab yourself some Wi-Fi and watch the world go wireless forever in 2018.

Yes

Nope, you must have an internet provider of some sort, which always includes a monthly fee.

Are you talking about a wireless router or modem? If so, then yes