For starters, no, the LG UltraFine 5k 27" display will not power the 12" MacBook (Early 2016) models.
As for being able to out put video to the LG UltraFine 5k 27" display, this is not officially supported by Apple. See Use the first gen LG UltraFine 5K Display with your Mac and Use the second gen LG UltraFine 5K Display with your Mac
However, it may be possible by getting a USB 3.1 Gen 1 digital video output to Thunderbolt 3 adapter (or a combination of adapters to achieve that outcome) and then running the LG UltraFine 5K 27" display at lower resolutions.
The problem you're going to face (besides the cabling involved) is that your MacBook is capable of external resolutions of:
- up to 3840 by 2160 pixels at 30Hz
- up to 4096 by 2160 pixels at 24Hz
The LG UltraFine 5k 27" display, on the other hand, is designed to work in the 48Hz to 60Hz range (although all its recommended resolutions are specified at 60Hz). See below table for Signal Timing specs:
As you can see, trying to find a sweet spot to run the LG UltraFine 5k 27" display from your MacBook looks challenging and probably not worth the time, effort and money to try as it'll most likely result in failure anyway.
However, over the years I have seen people far exceed what is officially supported by Apple in terms of various MacBook models and the displays they're connected to, so if you're happy to invest the time etc, it may be a fun project.