Will my mother recognize me on the Day of Resurrection if I act like her and attain her status, and will we accompany each other to the gate of Paradise, despite the verse: "On the Day when a man will flee from his brother, and his mother and his father"?

You must strive to do good deeds and ask Allah for acceptance, and supplicate for your mother for forgiveness and mercy. If both of you are among the people of Paradise, Allah will reunite you by His mercy and grace, even if your deeds differed, in fulfillment of His saying, the Almighty: "And those who believed and whose descendants followed them in faith – We will join them with their descendants, and We will not deprive them of anything of their deeds. Every person, for what he earned, is in pledge." The fleeing mentioned in the Quran will be on the Day of Resurrection due to the severity of the horror, but in Paradise, there is no toil and no exit from it. As for seeking knowledge, there are many ways now, and you can search for reliable preachers online.