General

I think during the Red event, you could do some quest and it gave you a free perm pet

There's a free permanent cake pet that comes bundled with Maplepoints, EXP present boxes, respawn passes, equips, etc. in a "Welcome back to Maplestory" gift box given to players who returned to the game after a few months of absence. My friend received one when he logged in two weeks ago after a four month hiatus.

As far as I know, you can't obtain one otherwise unless you purchase it.

You buy one.