Was Mannimarco the first lich?
Hm. I don't think so. He began in the Psijic order a little bit after the fall of Remans empire, so I'd be surprised if he did wind up becoming the first lich. Some of the Dragonpriests we encounter may be older than him.
Are Dragonpriests a type of lich?
I'd say so, though it appears the Nords streamlined the process somewhat. Certainly seems more consistent than most other's botched attempts.
When did Mannimarco become a lich?
Hm. Good question. Would the Psijics keep a lich around?
Why would Mannimarco become a lich if magic already extends his lifespan and he is one of the longest lived races in Tamriel?
Immortality seems to be a good enough boon, and besides, he was pretty obsessed with necromancy.
What benefits would Lichdom grant?
Immortality is usually most peoples goal, though it also allows them more time to roam Tamriel, amassing their own powers and continuing whatever hellish pursuit they decides to cook up.
Seriously though. Given the timeframe wouldn't Dragonpriests be the first liches?
Hard to say. I wouldn't be surprised if each race has their own take on the process.