Is it permissible for a young man whose heart is attached to a girl, and who is currently unable to marry her due to his young age, to ask her for her phone number so that he can speak with her periodically to check on her, learn about her condition, and see if she has received a suitor, with the intention of marrying her in the future?

Steadfastness in obedience and abstaining from what displeases Allah are reasons for the young person's success in obedience. You are permitted to express to the girl your desire to marry her in the future, within the bounds of Islamic etiquette, and do not exceed that. Conversation between a young man and a young woman is an open door to fitna (temptation/strife), and studies may not be an impediment to marriage. If you can marry her before finishing your studies, that is good; otherwise, cut off all relations with her so that your attachment to her does not affect your faith and religious devotion. Be patient and pious until Allah facilitates your affair for you.