Is it permissible for me to ask my friend to be righteous for me and to advise me, or should I suffice with supplication only?

There is no harm in a woman asking her sister in Islam to befriend and advise her, and to point out her faults so she can avoid them. This is a good deed, for the believer is the mirror of his brother. 'Umar, may Allah be pleased with him, said: "May Allah have mercy on a person who points out my faults to me."