Symmetric vs non-symmetric pairing based crypto I am trying to find a comparison of how different pairing-friendly elliptic curves perform (in terms of security) in real world applications;

I am using PBC library, and it has type A curves and type D curves (also , i am having hard time understanding how pairing types depend on underlying curve types, and which of them have been broken/ or are considered insecure at the moment;

Type A 

Type D

At first glance, there are 3 types of pairings, type 1(symmetric), type 2 (g1!=g2, g2->g1) and type 3; i understand that different algorithms require pairings to be either of type1 or type2 or type3;

I would also like to know more about why some algorithms are limited to certain pairing types.
Any references would be greatly welcome
This lecture by Dan Boneh should answer all your questions and more:

https://www.youtube.com/watch?v=F4x2kQTKYFY

ps. I saw you also had a question about NIZK proofs, so you should check out the full list of videos

https://www.youtube.com/playlist?list=PLXF_IJaFk-9C4p3b2tK7H9a9axOm3EtjA

which has almost 3 hours of lectures on Groth-Sahai proofs by Jens Groth which might interest you.