COS from H1b to H4 stamping

My husband recently laid off on H1b (his 60 day grace period is ending on August 25th). We are planning to file H4 COS for him (with my H1b). Considering this scenario, I have few queries:

  1. Can he go to Mexico/Canada for H4 visa stamping (once they open after December) after his 60-days grace period is done or he has to wait in US for his COS approval.
  2. Can he bridge/apply for another H1b visa transfer even his H4 COS is pending, considering he gets a job in another one or two months.