Powering arduino and node mcu
In principle not. However, the voltage regulators may become quite hot, since you are going down from 12 V to 9 V and 5 V (especially the step from 9 V to 5 V is quite a lot). It depends on the current (in (milli)Amps) how hot they get.

For the adapter it does not matter, if it is 1 A or 10 A, the microcontrollers will only take whatever they need. Only if the adapter can deliver less than needed by both microcontrollers there is a problem.

The voltage regulators are not of switching type I guess, so they will use the same amount of amperes. Assuming the Arduino Uno takes 300 mA (at 5 V) and the NodeMCU 200 mA (at 12 V), you can add them together: 200 mA + 300 mA = 500 mA. Since this is less than 1 A the adapter can deliver, you are ok.