While I admire the trust you display, I think it is misplaced.
In my experience, the more you do to secure your online communications, the more attention you draw to yourself. Your MAC address uniquely identifies your computer's network interface. The ARP protocol links your MAC address to your IP address. When your online activity becomes suspicious, or the subject of inquiry, you can not hide from ARP tables and man-in-the-middle exploits, no matter what software you install on your computer. Seriously, if you want to tell your mother you love her without anyone else knowing, do it verbally, in a secure location, and with audible white noise in the background.
You use a lot of terms you clearly do not understand.
ARPs are only layer 2, so only the switch your machine is plugged into has your MAC.
Not that that matters, MACs can be obfuscated (spoofed).
Not that *that* matters either, as that is not how you'd be identified across a *routed* network anyway.