In short, yes.
The exact method will vary a little, depending on your OS.
Open network settings > right click on your wifi adapater > under the 'sharing' tab, check "Allow other network users to connect through this computer’s Internet connection". *
*Phrasing may vary depending on your OS.
That should be all you have to do to achieve wifi "in" to the laptop and ethernet "out" from the laptop.
As for your bonus Q. That entirely depends on your perception. It's the 7th GT in the "main" line.
The studio were pretty adamant it isn't intended to be GT7 leading up to the launch: (http://www.technobuffalo.com/2016/06/11/gran-turismo-sport-e3-2016-trailer)
But pulled a full 180 later: http://www.digitalspy.com/gaming/ps4/news/a794751/gran-turismo-sport-is-gran-turismo-7-after-all/
Unfortunately, all that means is you'll have to wait for the next release & see how it's titled (ie will it be 7, or 8? Or are they abandoning the numerical elements, and will each release have it's own 'title'?)