Is marriage to a woman with whom one has secretly committed fornication, after repentance from fornication, Islamically valid? Does her guardian forfeit his right if he refuses to marry her off because he is already married? Is she entitled to refer her case to the Sharia judge to marry her to him? Is it permissible to agree that she will stay with her family after marriage?

You both have done well by repenting from zina. It is permissible for you to marry this girl, as long as you both have repented. However, her guardian's permission is required; otherwise, her marriage is invalid. If the guardian withholds consent (adhal), the matter should be referred to a judge to either marry her off or appoint someone to do so, or the guardianship transfers to the next closest guardian. It is not necessary to inform your family about the marriage unless doing so would lead to harm. You may stay overnight at her parents' home if you marry her correctly and no harm results from it. A man marrying more than one woman is permissible if he is capable of being just, providing for them, and fulfilling marital relations.