Am I entitled to file a lawsuit against my husband who abandoned me three months ago, leaving me at my family's home, and does not provide for me or my son, knowing that he takes our son every now and then? And what are my rights in this situation?

It is not permissible for a husband to abandon his wife and child without providing for them. The wife must demand this provision from him. If he abstains from providing and she finds that he has money, she may take her provision from it in a reasonable manner, as stated in the hadith of Hind bint Utbah. If this is not available to her, she may refer her case to the court to compel him to spend on her and her child, and to recover her past maintenance.