Dear colleague, voom was not designed for microarray data. .

1- If I have microarray data that background adjusted and quantile normalized. Is it necessary to apply voom function on it not for normalization but for log transformation and creating precision weight? or no need for that?

No. Please do not even consider voom.

2- Does the voom function provide access to other normalization methods? I mean if I run voom function at any data, is there no need to run quantile or loess normalization or can voom be conjugated with another normalization method?

No. Quantile would typically be performed on Affymetrix microarray data, while LOESS would be performed on that from Agilent.

In summary: I believe you are confusing methods between cDNA microarray and bulk RNA-seq.

Kevin