F1 OPT to H1B COS vs CP

I am currently on F1 OPT EAD starting my job in Mar 2020. My employer is applying for H1B. I want to know which is better, Change of status or Consular processing. The reason to opt for CP is to avoid SSN and healthcare taxes and freedom to travel outside US.

  1. Can I apply for CP and retain my F1 as long as I want?
  2. In case H1B in CP is approved, can I still extend my F1 under STEM extension and get H1B stamp once F1 OPT expires?

Thanks in advance for any help