Can I even use it to remote control my server? HP have iLO, but it's completely different beast, AFAIK. I've never heard about using Intel ME for servers.
If your PC doesn't use an Intel ethernet/wifi chip you're 100% safe from remote execution attacks because AMT only works with Intel chips.
AMT on the other hand provides its network functionality by hijacking the host's IP, and siphoning off traffic destined for its ports (16992 and 16993). This is one of the things that makes it scary, and just one of the differences between it and IPMI.
Source: I have worked extensively with AMT and built a semi-open-source Python management library for it in a previous job.
https://www.thomas-krenn.com/en/wiki/Nuvoton_WPCM450R_IPMI_C...
Oracle uses these: