How seamless is using a MacBook as a desktop replacement?

Before I take the plunge I want to ask some last questions. My plan is to use the 2016 MacBook as a highly portable computer (well, naturally...) but also connect it to the LG 21,5" Ultrafine display when I'm at home and use it exclusively on this screen.

My biggest concern is that it might not work as seamless as I'd wish. So here are my questions:

1. When I want to use the same wallpaper when I'm on the go and at home, would there be any problem because of the different image resolutions of the screens?

2. What about icon placement on my desktop? Of course I can fit a lot more icons on the 21,5" display at home. I usually don't have more than 20 files on my desktop, but I guess they will be rearranged everytime I decide to unplug the MacBook from the external monitor because of the lower resolution of the MacBook display?

3. Can I leave the MacBook's USB-C cable plugged in and put the MacBook in some sort of sleep mode that uses very little power while still being able to power the Macbook on with the Magic Keyboard? I wouldn't want to retrieve the MacBook out of the BookArc (that I am planning to buy) just to open it, power it on, close it and put it back into the BookArc.

4. Will there be any noticeable lag when using the 21,5" in 4k/60Hz mode? I would find that highly annoying although I'm not planning on gaming.

 

Thank you @Rapp, this was super helpful information. *thumbs up*

Now I'm only hoping for a MacBook m5 bargain before christmas.