change of status from H4 to H1 visa for same employer who sponsored my h1b

Hi Saurab, I had a valid H1b visa from employer A valid for next one year. My spouse also works for employer A in h1b visa. Since I could not find a job opening at US , I had to quit my job and got h4 stamping as my hubby is on h1b and planning to travel in h4 visa immediately. My h1b was not cancelled during h4 stamping . So can i still travel in h1b or not? However my employer agreed to recruit me at US in a month or 2. Hence I need answers for these questions. Please help. Q1: can employer A file change of status H4 to H1? Q2: is there any time period that I have to be on h4 before filing chnage of status to h1? Q3: how long does it take to get COS approved and when can I start working? Q4: can I look for a new employer B and can employer B file COS for me? Thanks.