I want to express my appreciation to someone who helped me, Can I say: I feel grateful to this person for his help on the project? (I don't want to use thank)
Your usage of 'grateful' is grammatically correct - an acceptable usage is
grateful (to somebody) (for something)
For example - I am extremely grateful to all the teachers for their help.
Personally I would say "I am grateful to...." - for me it seems more natural, but that really comes down to personal choice.
I really appreciate your help on the project.
I am really grateful to you for your help on the project.
Yes, you can.
I'm so grateful (to you) for all your help on the project.
BTW, I'll go for "I really appreciate all the help you gave me on the project"; the use of the appreciate is far more common and idiomatic.