小白兔,radiology pls help w/ H1B portability questions

Hi 小白兔,radiology and other gurus,

Really need your help!!!

I resigned from my company in Feb and transferred my status from H1b to H4. Now I found another company and they are not familiar with H1B sponsorship. So I need to do my research and educate them on it. I am new on this since my old company filed H1B for me before. I have a couple of questions and your help are greatly appreciated.

1.Is my understanding correct that i am not subjectd to H1B quota? ( last company is for profit one and I uses 3 years of H1B there)

2.Am I still eligible for H1B portability rule? H1 and then for a little bit of H4 and now H1. I know this is new H1 petition. I just want to let new employer now that I can work as long as the file I-129.

I was getting some conflicting ideas on this, and really confused me.

Thanks a lot!

德龙