Retrofit Wireless Alarm System

If you live in a very hot climate zone: yes. Otherwise not really needed.

See above or

Not for the nodemcu. it is powered via usb power supply.

A simple one if it is really needed at all. Depends on a good or bad manual for your alarm central.

Around 50W, temperature controlled would be nice.

Depends on your budget. Sometimes there is useless stuff in there.