Update:

I finally got the brake master cylinder out. Like David Hendy mentioned earlier about this 5mm hex bolts and the ASR pre-charge bracket can be removed, actually there is only one 5mm hex bolt and the ASR precharged 2 brackets. I used 5mm hext socket and came out with ease. Then the bracket came out easily through that the nut on the lower left side of the brake master cyclinder. I was then abled to removed the 13mm nut with more depth than before. It was tough to remove that 13mm nut, but slowly and surely, the 13mm nut came out. Also, another bracket came out of the top right of the brake master cyclinder Thanks!!! See the pictures, sorry about quality of the pictures.

I did a push rod comparison on the both the old and the new brake master cyclinder replacement. I felt both had the same enough of force pushing the rods. I wonder if there is a way to determine whether the old master brake cyclinder is defective or not by testing? That is another story there. Anyway, thanks to all for reading and responding back.

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