1. I play in all modes! Which to me is shocking because I thought I would never touch Tabletop Mode, but the amount of comfort that it allows is unreal. Just completely shocking.
In order of playtime, I'd say they're all really close but
Docked > Handheld > Tabletop
2. I use my Pro Controller almost exclusively. I haven't really trying the Joycon Grip, but I want to! The Pro Controller just never dies
Pro Controller > Dual Joycons > Single Joycon > Joycon Grip
3. I played Switch local multiplayer a LOT. The thing is amazing to play with other people and so easy to play both on tv and on tabletop.
Whenever I play with other people, the control options depend on the game and whether or not I'm actually going to meet people to play the Switch. If it's just "hey you want a quick round of Isaac/Puyo Puyo Tetris?" I use two Joycons because I don't carry around my Pro Controller with me at all times.
But if I'm heading somewhere with the intent of playing with others, I bring my Pro Controller and my Joycon Grip. If I'm playing with one other person, they get to use the Joycon Grip and if I'm playing with two other people, they split single Joycons.
I don't have a solution for four players quite yet, but that hasn't been an issue because I'm surrounded by people who own Switches.
4. I absolutely have played the Switch in handheld and tabletop mode outside of my home! Hell, I've played the Switch in handheld and tabletop mode IN my home too c: