Is it considered a sin to speak with an engaged girl and then become engaged to her after her first engagement is dissolved, knowing that my relationship with her began by offering her advice to overcome the problems of her first engagement?

Your conversation with the fiancée does not constitute an offense against her betrothed. However, your communication with her, as she is not your mahram, is impermissible except when necessary and with adherence to Sharia guidelines.

If the engagement is broken, you are permitted to propose to her, provided you were not the cause of its dissolution.

If the engagement is still valid, it is not permissible to propose to her while she is engaged to your brother, unless he relinquishes her or grants permission.