fall transfer (too old?)

No you will not be overlooked. Usually they look for younger guys to give bids to but if you look like someone that will bring a lot to there fraternity you will get a bid.

No. you should be fine. Even though you are 22, you are considered a sophomore by credits, and so you still have several years of commitment and time to give to whichever chapter you possibly join!

Guys can pledge at 22 for girls its not really a thing. Most your pledge class will be 18... will you really have anything in common with them? 22 is a bit old to join a sorority. Consider joining a club or inter-mural to meet new people.

I had 2 pledge brothers while I was 19 and they were 22, they're 2 of my closest brothers now, go for it.

Your bid is not guaranteed (no one's is) but I hope you immediately take part for your chance to welcome sisterhood and lifetime service into your collegiate years. There are many reasons a sorority willingly accepts an older student as a new member. Some national NPC sororities recently wrote on social media about their older new members, women who have served in the military or put-off school to help with family matters. If you decide against NPC recruitment, there are multicultural sororities on campus. The NAU greek life pages should be where you begin your informational journey toward the sorority life. Good Luck!