The ALPG for CoS should be out some time during the next week (assuming there are no delays). The CoS season doesn't start officially until March 1st (DDAL 4-1) and March 4th (CoS). Even then, the Season 3 ALPG does not expire until March 15th (or when the Season 4 ALPG is released, whichever happens first). Until such time as the Season 4 ALPG is released, the Season 3 ALPG is valid and should be used.
In respect to a LE Fire-Genasi Necromancer raising the dead - your friend is correct (in part).
DMs must allow any legal character option available to a character based on their story origin. There are no exceptions to this rule - precisely to avoid situations of DMs prohibiting variant humans, Elven Bards, Necromancers (or any other character option/combination the DM has personal issues with); in addition to avoiding issues of power creep.
- As such, playing a LE Fire Genasi Necromancer is perfectly legal, providing the character is a member of the Zhentarim or Lords Alliance and has the Elemental Evil story origin.
- The character can legally choose any spell from the PHB available to their character (at the appropriate levels), including animate dead and create undead.
- This character is prohibited from using any material out of the Sword Coast Adventurers Guide (including green-flame blade) as characters cannot mix content from the SCAG and EEPC
The DM does however, have a say as to how NPCs react to any spells cast, and is under no obligation to honor spells cast in previous games (or at tables with previous DMs). As such, the DM is well within their rights to say the character cannot start the adventure with one (or more) undead in tow, and instead ask them to collect each corpse (and cast each spell) during the adventure itself.
In fact, this is recommended due to the fact that the DM has no proof regarding the HPs of any given undead (except what the player says).
Depending on the spell, the DM may also be in control of the actions of any summoned creature. While the creature itself will follow instructions to the best of their ability and remain loyal to the PC, unless the PC has an option to take full and precise control of a creatures actions, usually they will use very simplistic tactics (and will often take the shortest, most direct path to a target even if it provokes Opportunity Attacks).
Finally, the DM can ask the player to tone down any behavior that is becoming disruptive to the table. Casting spells or playing classes that the DM disapproves of is insufficient grounds to call the behavior "disruptive", but should the character hog the spotlight or their turns take too long (leading to boredom from other players), the DM is well within their rights to step in at that point. As a guideline, I don't let any single character take more than 2-3 minutes on their turn before I instead ask them to take the "dodge" action. This is how long a summoner's turn should take as well.