Sufficing on the three fardh of ghusal

(I don't know whether I am a hanfi, shafi etc, so please answer accordingly)

The ghusl/ritual bath that we perform to become paak after menses, etc. have three farz/compulsory acts: washing mouth, cleaning nose, and pouring water all over the body. So if we perform ONLY and only these three acts and NOT perform the remaining acts like performing "Wuzu", washing wrists (not the one in wuzu), doing niyyat, etc. will our ghusl be valid and will we become paak?

Also, if I only perform these three acts and that too not in proper order (for example I wash my mouth and nose in the end or any other order), will my ghusl be valid and will my namaz be accepted?