Possibly yes. Out of the lavs I've used (DPA, Rode), the manufacturers had XLR adapters with the right electronics inside to convert 48V phantom power to plugin power (3-5V). An off the shelf XLR - 3.5mm female wouldn't work with those mics.
Then on the other hand, I had a look on the internet to see if I could find the product description in English and I found this: https://www.boya-mic.com/product/by-m1 . On that page it says:
"Foam windscreen, lapel clip, 1/4” adapter and LR44 battery included."
That's implying it has some kind of battery? Maybe it won't need plugin power at all? That's why I suggested that you check with the manufacturer if it needs it or not.
One final point if you go from 3.5mm to XLR is to make sure that the wiring of the 3.5mm side is right. The mic appears to have a TRRS connector and many adapters are TRS - XLR instead of TRRS - XLR. I guess also extra fly in the soup is that there's actually two different TRRS types, CTIA and OMTP, but the latter has dropped out of use mostly. The 6.3mm adapter looks like a standard mono plug, so that's circumventing that issue if your recorder has 1/4" jack instead.
The Zoom P4 does appear to record 4 channels simultaneously, yes. Although it's good to note that "2-In/2-Out Audio Interface" means that when you connect it to a computer it's only transmitting 2 channel stereo. If you use it as a standalone recorder the manual mentions " In addition to a stereo file ready to be used for podcasting, the recorded data includes separate files for the audio of each channel that can be utilized for editing after recording. "
The USB mic idea could work but again with some caveats. Generally audio software likes to record from a single audio device at a time. On a Mac you can join multiple devices into an aggregate device, which you can then use in the recording software. On Windows you'll need a third party software to combine them.
Finally I had a look at the mixer you had originally linked. It seems the manufacturer had another model (https://www.amazon.com/dp/B07NMHRSQQ/ref=emc_b_5_i) which mentions " 48V, 1.5V Phantom / Plug-in power modes " so that could be an option. But the way the selector switch is placed, does it give the voltage only for the first channel? It also mentions USB compatibility but it'll likely be 2 channel stereo only (" Master USB Audio "). Eh, dunno mate. All this China wonder consumer gear is giving me a headache. I wouldn't trust them personally.