Can I transfer H4 visa to H1B with the below situation?

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Hi There,
About me :

  1. Currently on F1 visa
  2. H1B didn’t get picked 3 times
  3. My F1 visa expires in June 2021
  4. Planning to get H4 through my spouse
  5. Spouse does not have i140 yet but will get it in 12 months

My questions :

  1. Can I look for cap-exempt H1B job once I have H4 visa (without EAD) ?
  2. Can you explain how the process of converting H4 (without EAD) to cap-exempt H1B works ?

A huge thank you in advance for your response!