I think
@Charlaquin gave the best explanation.
Personally, I would say you can cast spells that are on the Wizard list, that you have.
You can cast spells that are 1st level, or 2nd level, or 1st level that are cast at 2nd level.
And that's it.
But I am not too worried about the edge cases on an 18th level ability. If you've made it to 18th level, and you're worried about the synergies (because if they are MC synergies, that means you are actually at least 19th level), then I am sure that there are a lot of other game-breaking issues that might already be at play that are more worrying than this one.
MC is not a concern (since this is 18th level). It is spells through feats and species that are the real concern although the rules would apply for MC as well. The character in question has the following from features other than EK spellcasting:
Truestrike-Magic Initiate(Wizard) (works, becuase on the Wizard list)
Firebolt-Magic Initiate(Wizard) (works because on the Wizard list)
Tasha's Hideous Laughter-Magic Initiate(Wizard) (works because it is on Wizard list)
Dancing Lights-Drow (works because on the Wizard list)
Faerie Fire-Drow (does not work, not on Wizard list)
Darkness-Drow (works, on Wizard list)
Levitate-Drow High Magic (works, on Wizard list)
Detect Magic-Drow High Magic (works, on Wizard list)
Dissonant Whispers-Fey Touched (does not work, not on Wizard list)
Cause Fear-Shadow touched (works on Wizard list)
Invisibility-Shadow Touched (works on Wizard list)
Command-Magic Initiate(cleric) (does not work, not on Wizard list)
Guidance-Magic Initiate(cleric) (does not work, not on Wizard list)
As an aside all of these spells are on Charisma, not Intelligence. The PC has a 20 Charisma and an 8 Intelligence.
Dissonant Whispers is the one they really want to cast as part of the attack action. Hit with an attack then cast DW with disadvantage on the save and then follow it up with Warcaster-Cause Fear as a reaction when the bad guy runs away, keeping him away. You still have action surge and a bonus action, each also potentially with a spell (as long as you only use one slot).