A:AnswerMake sure you are using the charger that came with the Switch or a different Nintendo Switch branded charger. I've heard any other regular usb c chargers don't work with these.
A:AnswerNo. The Switch requires the extra power to have video output. Outputting and up-scaling from a 720p image to a 1080p image on your standard TV uses more power than the Switch can do on its own. Be sure you use the OFFICIAL Nintendo Switch A/C adapter otherwise you could risk frying your Switch.
A:AnswerNo, it does not. The Switch Lite's hardware is completely different than your standard Switch. It is not possible by any means to output to a TV from a Switch Lite though a direct connection. There has been several Youtube videos out there on this subject.
A:AnswerThis is caused 'cuz the power is insufficient, or the HDMI cable you're using sucks. Try replacing the HDMI cable, and then using a Nintendo branded Switch charger to power the station. It could just be the TV's HDMI port sucks as well.