Hello, everyone!  You all can call me Katherina, and I'm new here. 

About this time last year, I was forced to cut off nearly all of my hair, thanks to a very bad over-the-sink dye job.

Now it's a pixie cut.  A very comfy, carefree pixie cut, I must say, yet I miss my regal braids and French twists.   

I'd like to grow my now dye-free, medium blonde hair to perhaps a few inches past my shoulders.  Any tips for a Rapunzel-in-training?  How can I keep myself from chopping it all off in frustration?  How can I gracefully grow out my bangs, without looking like a punk rocker?

I need help from as many hair experts as I can find... and I believe that I've come to the right place. 

Hello and welcome to LL!  Glad to have you on board :
Angel has done a good job with her suggestions There's a lot of info. here for you to read.  I'm sure that if you ask questions alot will offer their advise,experiences and suggestions.  We are all learning from one another and trying to either maintain or grow long healthy hair!
Just make sure anything you use to keep you bangs out of your eyes while growing them out is hair safe!