The way in which this man has been behaving with you is to be considered wrong, especially his talking to you every day. You should avoid that and your mother should ask him to stop it. If he is sincere in his desire to marry you then he should behave in the manner prescribed in sharee’ah, by approaching your wali (guardian) to propose marriage to you. If you do not have a Muslim wali, then your wali is the Muslim ruler in the land where you live. If there is no Muslim ruler, then the wali is a person to whom other Muslims refer, or one who is influential among them, in the place where you live, such as the director of the Islamic center or the imaam or khateeb. He should check him out and find out how fit he is to be a good husband or otherwise.
With regard to the things that you should look for in a husband, you will find the answer to that under question no. 5202. You can also refer to question no. 389 and no. 2127 to find out the conditions of a wali for a Muslim woman.
We ask Allaah to make it easy for you to find a righteous man who will help you to obey your Lord… Ameen.