It's hard to get a specific Family in AOTR because there are 28 total Families plus one currently-unobtainable Secret Family, all pulled through gacha-style Spins with no way to target one directly, aside from a pity system guaranteeing at least Epic rarity by 400 spins.

No, not all Families let you Titan Shift, Zoe and Ackerman specifically cannot Titan Shift at all, though Ackerman makes up for it with strong ODM-focused bonuses instead.

The Serum needed to Titan Shift is genuinely rare, the rarest one drops at roughly 0.184% and only while playing on the hardest difficulty setting.

Yes, you keep the Families, Serums, and Artifacts included with my purchase, exactly as shown in the listing.