Is it permissible to speak with a married female neighbor who is suffering from marital problems, and to offer her advice or comfort, with the intention of marrying her if she gets divorced?

The temptation, in your case, is not safe due to the hidden intention you harbor in your heart to marry her. Therefore, we advise you to stay away from this woman and not to speak with her. Your mother's advising her is sufficient. If you wish to help her, you should advise her husband and explain to him the error of his actions, and call him to observe prayer and repent from sins, if possible. As for her, beware of engaging in unnecessary conversation with her, as it opens a door to great evil.