What should I do, given that the girl's family refuses my marriage to her unless she completes her studies, while I continue to meet with her and talk to her? And is it permissible for me to write the marriage contract with her?

A Muslim should refrain from speaking with and meeting foreign women before incurring God's wrath, and should not preoccupy himself with them. The path to marriage is well-known. If her guardian refuses to marry her off at the time he desires, then he should be patient if he truly wants her; otherwise, he should look for someone else. A marriage contract is only valid with a guardian, two witnesses, and an offer and acceptance. What some ignorant people do with an invalid contract is a devilish trick to legitimize fornication. There is no objection to trying again with her guardian to request her hand in marriage.