There will be a new gamepad for the NX, so whatever that means to you.

Of course you can. The remote functionality is built in, and it doesn't need the Wii U to be on to use it. Unless they come to your house and break it, you'll be able to use it for a remote.

you'll probably be able to use the remote, netflix and Internet for a long long time.

-Now internet will depend on how things evolve and the support behind the browser
-Same goes for Netflix
-For the remote, you can't be sure that if you change your TV for a newer model it will be compatible with the remote.

But frankly, I don't think you will care about all of that 2/3 years after Nintendo stop to support it.
Me I already stopped using netflix on WiiU, mainly because my TV has an ethernet connection.

I hope so, the internet browser is too good to pass up, and it can only get better so long as the GamePad is usable.
(I'm typing this on my Wii U)

I'm guessing the NX will be backward compatible but will require you own a gamepad to do so. That'll keep Wii U owners happy and mean they can try and sell gamepads at a reduced price to NX owners.

I am sure it will. The gamepad most likely will be incorporated into their next home console in a lesser role.

I will be using it on my pc as a tablet when it gets hacked

Should be able to.

Nintendo isn't going to anchor to such an expensive  peripheral that isn't bundled with the consul.  especially when it affects not only wii u had ability, but 3DS and DS as well. The gamepad is returning.

I think Nintendo would still integrate the Wii U gamepad and able to connect it to NX like how WiiMote is used for Wii U. or Gamecube controllers to the Wii and Wii U. Hopefully no more WiiU Gamepad dongle just for connectivity to the NX.