As Salamu Alekum sister Sakeena
First, I wanna state that I'm a brother not a sister
. In fact, "Ibn" means "the son of", as in "Omar ibn Al Khattab" or "Othman ibn Afaan" or the great scholar "Ibn katheer"
"Ibn Syena" himself was one of the most prominent muslim scientists and physicians early in islamic history.
Well, anywayz, regarding the Dawah and your friend, I wanna tell you at first that it's not you or me or anyone else who guide people to the right path, it's Allah alone. He (Subhanahu Wat'ala) says: {Verily! You (O Muhammad SAW) guide not whom you like, but Allâh guides whom He wills. And He knows best those who are the guided} (56:28) Al Qassas. You can do your best, in every possible way, doing it with great sincerety and devotion, but still the final result is up to Allah (SW) alone. Don't you remember the story of prophet's uncle "Abu Taleb", who looked after Muhammad (saw) after death of his grandpa, defended him long time till his death and was helping him spread his message, and whom Muhammad (Saw) loved him so much, yet he wasn't muslim. Muhammad (saw) tried everything with him to make him a muslim, but he refused it, and died as (mushrek) or polythiest. Prophet Muhammad (saw) was very desperated for this, he was really annoyed he couldn't save his uncle who helped him much all through his life, brought him up as one of his own children, and who was a great support to him, he couldn't save him from (kufr), so the previous verse {Verily! You (O Muhammad SAW) guide not whom you like, but Allâh guides whom He wills. And He knows best those who are the guided} was released to him.
Well, think the point is clear, no? So..you've to keep trying with your friend if you really love her and wanna save her, in a good manner and with good example, try not to offend her, never call her ignorant, stupid or anything negative: {Invite (all) to the way of thy Lord with wisdom and beautiful preaching; and argue with them in ways that are best and most gracious: for thy Lord knoweth, best who have strayed from His Path, and who receive guidance} (125:16) An Nahl. Please remember that you have to be very patient, may be one day even if you're apart, she'll remember your words and preachings due to some life event, and she'll come herself to you. Rememebr also to make lots of Dua' for her, it's the stongest (weapon) we have.
well, regarding your mom, of course there are lots of things you can do for her, just don't leave her alone, don't you want rescue her? All of what was said about your friend is applicable in a way or another to your mom, but the most important of which is DUA' (prayer or supplication to Allah) to guide her. The second most important is you yourself being good example and representatve of Islam, as she sees Islam only through yourself. I already heared a lot of reverts stories whom their parents reverted too when they saw a good example through thier offspring.
May Allah help you and give you strength and patience
Wasalamo Alekum Warhmato Allah
