Is the client letter with duration is important for H1B amendment?

I changed from F1 to H1 and I have H1B upto 2015 September, I changed the client after I got H1B. Now I am planning to go for stamping, as per the new policy I have to do H1B amendment since I changed the client. My questions are:

  1. I am working in client location, client couldn’t give letter and the middle vendor will give letter. That letter doesn’t includes my name and duration, it only includes agreement between client and vendor. Is this safe to apply with this letter?

2)The letter states that vendor will control the work, my employer stating that my employer will control my work not the vendor. It would be risky to apply with that letter since employee employer relation is not proper. Is that correct?

3)Is H1B amendment is same like reapplying of H1?

Don’t mind if my words are bit confuse and Thanks in advance