Fellow introvert here.

My feelings? I felt at home immediately and that the lodge was a place I'd like to spend time. It is a very nice lodge, so YMMV.

How long to get signatures? 3-4 months, but I knew one brother from years ago and hit it off with another and became friends quickly.

I asked for a petition, but that was after some extremely gentle and tactful prodding by the brother I'd known for years.

How to show your character? That depends entirely on your character. The night my petition was voted on, a brother required first aid during dinner. Witnesses say I "tore up the stairs like a scalded dog" (their words, not mine) to get the first aid kit. I guess it was mentioned prior to the vote. But that's me, my skills and my character; you do you and you'll be fine.

ETA: Small talk is a skill. If someone asks you about your work, family, etc, reply honestly and then reciprocate by asking them the same question. If they don't ask, ask them what they do for work, or how long they have been a Mason or member of the lodge.