Is the marriage contract considered valid and Sharia-compliant, even if it is kept secret from the girl's sister or the public? And does the ruling on divorcing the wife apply if there has been no intimacy for certain months, and is it sufficient to be in the same room, house, or bed, or must there be intercourse?

You both did well to cut off the forbidden relationship between you, which is a fundamental condition for repentance. You must complete the conditions of repentance with regret and a firm resolve not to return to it. Marriage is the legitimate solution for those who love each other, as the Messenger of Allah, peace and blessings be upon him, said: "There is nothing better for two who love each other than marriage." Marriage has conditions for its validity, the most important of which, according to the majority of jurists, is the guardian (wali). As long as you have not consummated the marriage with her, it is better to annul the current marriage contract and then renew the contract with her guardian. If she does not have a guardian, the matter should be referred to the court so that the judge can marry her. Marriage with a guardian and witnesses is not considered a secret marriage, and delaying the consummation of marriage with the wife does not invalidate it.