Would using an application fee waiver affect my admission result in a negative way?
The people in the program will evaluate and score your application. 

They won't know whether the fee was waived, nor are they likely to care.

They will know if there is no GRE score. For some programs the GRE score is important, for others it is not. 

You will need to ask the programs that you are considering what there policy is. GRE waivers are usually in lieu of other evidence (such as a strong work history, previous graduate degree, performance on some other graduate test (MCAT, GMAT, etc)).