1. Is it possible to turn off the screen on Ultra, or can the screen turn off itself after a while?
You can turn it off completely. I don't think there's an option, yet, to let it go to sleep after a defined period of time. Might come later, perhaps or perhaps not.
2. How many PEQ bands exactly, 4 or 10?
10 bands. Either 10 bands applied to both channels simultaneously or - if you prefer that - 10 bands per channel. As of now, the WiiM automated room correction supports simultaneous L+R channel PEQ, only. Independent channel room correction is currently in public beta (but has just been broken with version 2.11.6 of the WiiM Home App. It will surely be fixed with the next release, but might still take some time until it makes it into the production firmware.
3. Now I use a Chinese DAC and a D amplifier to watch TV and listen to music from my smartphone, but I want to use room correction.
If you can use third party software like REW or HouseCurve, all of the above talk about stereo or L+R RC doesn't matter anyway. You can manually set the PEQ filters, then either per channel or combined.
If you want to rely on a simple automated process for RC, then - as pointed out by
@morillon - you should be aware of its limitations. Depending on your room and your (phone's) mic the results may be beneficial or not so much. In any case it makes sense to restrict the frequency range RC is working on.
WiiM's default is rather on the generous side (40 Hz to 4 kHz), but you can easily limit this range further. Also, max Q (default: 10) and max gain (default: 10 dB) are a bit on the high side, but (again) can be changed easily.
In one sentence: Be prepared to play around and tinker a little.