Dear sir,
Child marriage is not invalid marriage since inception. But it can be made invalid if the wife proves that her consent was obtained by fraud or force. The relevant provisions are Section 5 (iii),12(1)(c) and 12(2)(a) of Hindu Marriage Act, 1955. (You can read them if you wish to know in detail).
However, i would like you to know that she has made a long delay in filing a petition for nullity of marriage. The courts are unlikely to cancel the marriage now. Specially when her guardians will say that they gave a valid consent.
Next alternative is to obtain a mutual consent divorce (if the husband agrees to do so) or to file for a divorce on the ground of cruelty mentioned under Section 13 of the Hindu Marriage Act. She cannot marry you until she gets a divorce.
Answer to all your questions:
1. Yes
2. No. Marital rape is not an offence in India. Moreover you cannot prove such act which happened 7 years ago.
3. Registration is not mandatory as a proof of marriage in court. There are lakhs of couples of do not get their marriage registered. If the other side can prove that they followed the custom of taking 7 steps.. The marriage would be recognized in courts.
4. Forgery is punishable with two years. And limitation period for filing complaint for offences punishable with less than 3 years is 3 years. Unfortunately there is a long delay again.
5. No. You cannot get married untill your wife obtains a divorce from the previous husband. Even is she converts to Islam and marries you, she can be convicted of bigamy.
You can proceed by convincing both husband and wife to obtain mutual consent divorce. She can convince the husband by stating that she will not take any alimony or file a criminal case against him.
If that doesn't work then ask her to collect all evidences of cruelty and file a divorce on those grounds. Please remember, the Court will not believe her unless there are evidences.
Hope this answer helps.
Best wishes.