For the ESP8266 i can confirm that you can use the arduino ide with the correct packages.
I did it a couple of time to play with the ESP8266 and some neopixel clones but i used an already made devboard like the NodeMCU.
Glad to hear from someone that already had a go with this combo! The NodeMCU looks perfect for me as well. It's fairly cheap, and even comes with its own 5V to 3.3V converter. That makes the PSU situation a whole lot easier for me. And it even has USB already built in and ready to use - cool!
Concerning the SK6812 @3v3 it worked well from me. The led strip will accept the data signal at 3V3 even if it's powered with 5V.
But If you really want to push the signal to a 5V one, you can use a "level shifter". You'll find already made modules with 2 to 8 channels on aliexpress. They're really easy : you put the 3v3 lines and 3v3 power on one side, and you put the 5v's on the other side.
I did not expect that it would work at 3.3V at all. I'll have to try this though, since some of my strips will end up being about 7m long with no chance to run wires anywhere but to the strip's ends. But a level shifter sounds easy enough to wire up, thanks!
I will order a strip and a NodeMCU and see how far I might get. Huge thanks!
What remains are my concerns about my 3rd point. A strip with 30 RGBW LEDs/m is said to have 9W/m. That gives me 63W for a 7m length. WAY too much, considering that my strips will be just 30cm apart. I want to illuminate my living room, not blast my eyes out

My hope is that I could do with about 1/4 of the max power, and supply 4x 7m of strip with a 60W PSU, and my software making sure that the sum of the brightness in every such block doesn't exceed 1/4 of the sum of the maximum. Which is where the PWM comes in: If too many LEDs peak at the same time, I will potentially exceed the max output of the PSU by 4x (absolute worst case) for a new ns or ms. What are the chances of the PSU surviving this, and/or how could this be "smoothed" without having any direct control over the PWM?