You will need one of these:
https://www.overclockers.co.uk/tp-link-5-port-gigabit-easy-smart-switch-tl-sg105e-nw-134-tp.html
No.
7 useable ports. 4 on the switch and 3 on the router (as one goes to the switch)
Get a gigabit switch
I have not looked at switches for a while, can you get slower switches (ie 10/100s) these days?
It's a POE input. You can use it to power the switch instead of the AC adapter.
Judging by your original post you're looking at devices that cost far more than you need to spend. You just want a basic unmanaged Gigabit switch (usually under £20).