Symmetric vs non-symmetric pairing based crypto
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.