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Dear brother,
From Quranic point of view
Both of you fear Allah and believe in HIM alone
For Allah shall be the sole witness for the marriage between you
Your parents shall have no decision in this but to accept
A witness from both the sides may or may not be essential except for the sake of social identity
You have every obligation to do good to your parents; your 'wife to be' shall accept this
You have to get married if you fear you canot maintain the limits of being together
Nothing wrong in keeping this marriage a secret, for you want to do good to your parents
Live together until things get well
Above all this, once you have decided to get married ENTRUST YOUR WHOLE AFFAIR WITH ALLAH. For He loves those who entrust their affairs with HIM. HE is all knowing; Merciful
To conclude whatever you have written in your post is perfect and well in accordance with Quran. You are already well guided by Allah. Masha allah
May Allah Bless You, the couple
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