1 - Long wires are fine, I've had wires extend out to almost 15 meters so your 2m is ok. You will be fine using 22awg wires at that length and power draw, or 20awg to be safe side.

The longer you go and more amps you draw, the thicker the wires need to be because thinner wires will create a lot of resistance and will get overheated and can potentially burn thru the wire jacket. Here's a reference: https://quinled.info/2018/10/20/wire-thickness-needed/

2 - Your calculation is correct, but you will find that in practice, you will not draw nearly as much as the rated power of the LED strip. This is because there is no combination of settings from a normal controller that will cause all RGWWW LEDs to be run at max simultaneously. You will likely be using half of 60w.

3 - Mean Well is a good brand for power supplies. They are rated to run continuously at their stated capacity, unlike cheaper no-name ones. I have used their LRS series with good success.

https://www.amazon.com/LRS-200-12-Switching-Supply-Single-Output/dp/B0131UU9E2/

However your need is likely much less, so one of those 12v enclosed DC power supplies that plug into the wall will work.

https://www.amazon.com/Adapter-100-220V-Switching-Security-Accessories/dp/B0711Q5B49/

https://www.amazon.com/MEANWELL-GST60A12-P1J-Warm-White-Light/dp/B08VW9S99Y/