Can I connect my 144hz monitor to a gaming laptop and then also set 144hz?
Yeah yeah As long as the graphics unit in your laptop supports this output.
As long as the performance of the laptop is sufficient (which it should) this is possible. In desktop mode you will always reach 144Hz, while gaming probably less, but it depends heavily on the laptop.
Ryzen 5 3500x and gtx 1660ti?
It depends on what the laptop supports. Many laptops are only capable of 1080p60.
Most older games can easily be played at 144Hz.
Yes, if the display interface on the notebook allows it.