Is it a sin for a young man and woman to make a promise of marriage if their means of communication are cut off and the matter is limited to that promise? And is the young man sinful because the girl rejects other suitors for his sake?

If you promised a girl marriage, and the matter was limited to a promise without a relationship between you, then there is no blame on you for that, and no sin in her rejecting other suitors if you are sincere in your intention to marry her. However, if you are currently unable to marry, we advise you not to tie the girl to you, because delaying marriage may harm her future and cause her to miss a suitable marriage opportunity. Furthermore, marriage is not valid except with a guardian (wali), and her guardian may refuse to marry her to you. If a promise is unavoidable, then it should be with the guardian's knowledge, meaning by formally proposing to him for her hand.