What is the active MAC Address of my computer?

Use ip instead of the outdated ifconfig. Example:

ip addr show

...
2: eth0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast state UP qlen 1000
    link/ether 04:7d:4b:28:51:33 brd ff:ff:ff:ff:ff:ff
...

FINDING: The MAC address of network interface/adapter eth0 is 04:7d:4b:28:51:33.

I am not exactly sure why this happens, but I have seen it before too.

You are right about the MAC address -- it's the one in eth1.