Any WILL can be challenged/contested, on merits.
In Mumbai, it being a presidential town, it is mandatory to probate the WILL.
If there is no WILL left by your father and mother then both of the brothers (as per your post there is no other child than both of you) have equal share in estate left by your father and mother, including but not limited to two flats e.g. bank FDR etc even if nomination is made.........
All of your queries have been properly addressed.
Now you may proceed further under expert advice of your able counsel specializing in family/revenue/property/civil matters.
Needless to mention you can also contemplate same action as your brother and demand equal share in property being enjoyed by your brother, provided your father has not left a valid WILL in favor of your brother. If any WILL is left that needs to be probated and you will get the notice. The society is under obligation to ask for probate of the WILL, if any.
Certainly an amicable family settlement (registered) is the best option for future.
You may proceed as deemed fit at your end.