No, a flat-screen TV should be transported upright, in the same orientation it normally sits, since laying it flat can put uneven pressure on the panel and increase the risk of cracks.
Most people pack electronics the day before or the morning of the move, since you want to minimize how long devices sit unused, but label cables and take setup photos a few days ahead so you are not rushing.
It is better to use a soft cloth or blanket layer against the screen first, then bubble wrap over that, since direct contact with bubble wrap can occasionally leave marks on some screen coatings.
Yes, laptops should be fully powered down rather than left in sleep mode, since a sleeping laptop can generate heat inside a sealed, insulated box during the move.
Place screws, brackets, and mounting hardware in a labeled resealable bag taped directly to the device they belong to, so you are not searching for a tiny screw days after you have unpacked everything else.