This looks to be entirely up to DM discretion.

There are two equally valid positions on this and the rules do not refute either one.

The first is that this is a completely separate spell, and slot, and that the two have no overlap with your casting class. The spell you learned and the slot you obtain are kept separate from the class spells if you have levels in that class.

The second position is that it is a class spell, from your class list and you can retrain it as you would when you take a new level in that class.

The second position is mildly problematic in that you can continue to obtain higher level spells with the retraining, and it may lead to this MC being simply the obtaining of another 1st level spell slot, rather than feeling like a mini MC.

The first position is problematic in that it introducing additional bookkeeping and may be perceived to be overly harsh and pedantic.

In my games, I think I would allow the MC feat to simply be an additional first level spell slot and allow the spell to be retrained if it's from a class that allows that and you take levels in that class. I would probably not make them remember which spell goes with their MC beyond that the extra slot must be a spell from that class. This may be too lenient for some games though.

No, you can't cast it using a spell slot.

Spells you can cast because of your race aren't spells you know, and thus can't be spells you prepare. Per the PHB (p. 201, "Known and Prepared Spells"):

Before a spellcaster can use a spell, he or she must have the spell firmly fixed in mind ...

... and it goes on to describe some of the class-specific variations of knowing and preparing spells. But in any case, having a feature from your race or class that allows you to cast a spell isn't the same as knowing the spell.

This is spelled out clearly in the multiclassing rules for Pact Magic quoted in the question (PHB p. 164; emphasis mine).

If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.

Likewise, the Drow Magic trait clearly distinguishes the known cantrip from the merely castable other spells (PHB, p. 24; bold for emphasis mine):

You know the dancing lights cantrip. When you reach 3rd level, you can cast the faerie fire spell once per day. When you reach 5th level, you can also cast the darkness spell once per day. Charisma is your spellcasting ability for these spells.

If the intent of the rules was that Drow also knew the non-cantrip spells, it would say so.