When the gpu is plugged in did you move the dp cable to the gpu?

You will have to make sure is a cellular USB dongle not a WiFi one, but should work

Not sure about that specific TV, but as TVs get older they will stop having support for current and older apps.

I would recommend looking at a Google Chromecast 4k, then when it gets old you can swap it. https://www.bestbuy.com/site/chromecast-with-google-tv-4k-snow/6425976.p?skuId=6425976

With the laptop plugged in and the monitor plugged in try pressing the win+p and selecting duplicate or extend

You would need an additional modem If you wanted You “own” Internet. If you want a better connection but not pay for another internet, you could look in to a MOCA adapter kit or a powerline adapter kit