1) Will H4 stamping have affect on my existing valid H1 visa? Can they totally cancel it? Or will just make it invalid?
H4 will not impact H1B, however, they may cancel h1b on the passport at times
2) Or both H1 and H4 will be valid but I can enter US only with one status?
if they haven't cancelled, you may choose h1 or h4 to enter
3) I have plan to search project on H4 status when in US, in my company A itself. When I get project, can I change status to H1? Is it legal?
Yes, your new employer will file an h1 using previous h1 with COS
4) For H4 stamping, being a H1 holder, should I carry any specific documents from my company?
No, h4 stamping needs h1b principal applicants docs (Spouse docs)