Confusing situation applying for PR (EEA3)

Hi there,
I've been procrastinating applying for eea3 due to our complex situation, but finally I've got round to doing it, but need some advice.
My situation is clear, eu national, been here for 8 years, first 2 jobs with Wrs then been working for the same employer for 6.5 years.

However my wife's situation is not so clear. She's been in the uk since 11/2006, worked till 09/2009 (she's got WRS as well) then my first son was born in 11/2009. Then the second one in 10/2011. Wife has been home with kids basically since 09/2009 (on maternity leave till 08/2010 then left the company). She also worked 6 month in part time in 2014, but basically she is a housewife.

My questions:
Can we both apply for PR? Or does she automatically get it after me?
Should I apply on behalf of my kids (and pay the 2 x £55 for it) or just mention them in my application and send their birth certificate? Do kids under 18 get PR automatically when their parents get it?
Any help would be much appreciated! Thank you!