Speak to the NPC and it'll probably take down your character name/acc id. Then later on, someone from WP will internally access that account during maintenance and set the character's homunculus' intimacy to just below Loyal, around 910.
If you already have a loyal homunculus then don't sign that character up for the event by speaking to the NPC. If you feel as though you're missing out then why not make an alt Alchemist, create a homun and sign it up? Or kill the homun on your main and create a new base.
Not sure about the two separate dates for the event. Maybe they envision a large response and don't feel as though they'll be able to get everyone's homunculi done in one maint.
thanks for the reply..another questions...is it the event is for homun or homun S or both? is the 22/10 is for non evolve homun and 29/10 is for evolved homun or maybe for both?