1. Yes. It includes all applicable spells from the
Player's Handbook, Elemental Evil Player's Companion, with a few from
Xanathar's Guide. We didn't want to require people to purchase or have resources outside the core three books, so we consciously decided not to include material from
Tasha's Cauldron (for example). We will be releasing the spell lists as a web supplement, complete with spells from all official sources, soon after the book is released.
2. In our work the Sha'ir is an archetype, not a class, and a member of any class can become one (this is what we mean when we describe reintroducing character kits; more on that in a fuller answer below).
But to more directly answer the spirit of your question, regarding a spellcaster who relies on a genie familiar to gain and use spells, our take hasn't changed since we initially published it over two years ago. You can get it for free if you like:
The Sha'ir at DMSGuild.
Our take is a Noble Genie patron Warlock, with a Pact of the Lamp. This version has a gen (mechanically derived from an imp or quasit) that can fetch spells like it did in 2e. We also provide methods of implementing the concept using a Sorcerer bloodline (Genie-Blooded) and Wizard arcane tradition (the School of Genie Lore). We worked on a Bard option too but it died on the vine during playtesting.
The Warlock and Wizard implementations are in the Sha'ir document I linked above; the Warlock is also in
Midnight in the City of Brass along with the Sorcerer bloodline.