On the NUC boards with mSata, the mSATA port (PCI Express Full-Mini Card) for for SSD support. For other purposes, the board provides PCIe Full and Half-Mini Card connectors.
1) Yes, that full size port is a mPCIe port that is mSATA capable, not the other way around. All mPCIe devices will work in that port.
2) That's the hard one. You can grab a fat usb thumb drive, install the os on it, then setting the boot priority to boot from usb first. Downside is having to take up one of your usb ports all the time. Using this fat boy in the frontal usb 3.0 port in one of my HYE's and I'm pleased with the performance: Kingston HyperX DataTraveler HyperX 3.0 128GB USB 3.0 Flash Drive Model DTHX30/128GB - Newegg.com
3) Another, more hardcore option is to frankenstein your unit by running a mPCIe extender card out of your half size slot and running your full size card outside the case. I totally didn't have to build a dust cage for one of my units or anything... lulz