Indeed, but nowadays we just say “install” because it’s so easy 
Well all esp’s come with wifi (some come without atenna actually) and for ethernet you need a esp32.
In general a $2 D1 Mini (esp8266 - wifi only) should actually cover your needs and comes with onboard serial and micro-usb (or usb-c for v4) connector.
About the “right connections”: ESP’s have plenty of GPIO’s - depending on your needs you can also add port extenders or (in case you use a esp82xx) upgrade to a esp32 (some boards include Ethernet/PoE btw.) 
Might be (I have no idea actually 
) but I expect that most of the solutions only allow you to “own” the hardware and the software part will be a black box forever (including whatever limitations they have). On the opposite ESPHome allows you full ownership of your esp’s and is highly expandable. For example you could add Display and some controls to your esp and it will able to control stuff that way 