Moving from H1b Cap-Exempt to Cap

[H1bWorker]

Hi, 

 

Currently I have a H1B Visa from a cap-exempt employer (research oriented). I wish to change my employer (corporate), which would need me to have a h1b visa non cap-exempt. I would like your advise on the following issues. 

1) To work for a new employer, corporate (non cap-exempt). Will they need to apply for a new H1b in 2018, get it approved before I can work for them? 

2) Can i personally apply for H1B (non cap-exempt) without an employer offer?

3) if NO, the scenario would be to get an offer before 2018 H1b applications and wait for the h1b approval and switch there after? Is there any other way?

 

Thanks in advance for all the help you provide!