My opinion on your queries are as under:
a) Is extra marital affair adultery the same thing.
Opinion: Affair and adultery both are different, affair is only chatting, kissing, talking, traveling but if there is any intercourse then adultery will be there otherwise not.
b) In case of filing a divorce, are they covered under different section of law
Opinion: Divorce can be filed as per section 13 of Hindu Marriage Act-1955
c) There are other evidences like mobile bills which shows her involvement with someone. Are they enough to prove either extra marital affair or adultery.
Opinion: It is only the affair and can not prove the adultery.
d) If she does not give me divorce then what is the way out. Is it possible that court decides that now we cant live together and dissolve our marriage.
Opinion: Judicial separation u/s 10 of HMA is another option and after one year of legal separation the divorce can be grant to parties.
e) She is 100% at fault, still I have to give maintenance to my wife and my daughter while the divorce case goes on. She took my daughter forcefully (6 yr old).
Opinion: maintenance is based on the ability of the person, for child you are bound but if she is able to maintain herself then she is not entitle to get any maintenance from you.
f) She is not earning but highly qualified. Do I have to pay alimony for one time settlement
Opinion: It may be possible at the time of divorce.
g) If I have proves, like above, then how much time does it take to get a divorce.
Opinion: Mobile bill, chatting are not strong proof to prove adultery hence no value, but cruelty can be proved by these documents.
h) Can the above proof be contested.
opinion; It may be.