All warlock spell slots are the same level (PHB p.107, under the Spell Slots section). As they gain warlock levels, warlocks eventually reach their maximum of 4 spell slots (at the 17th level of warlock), and their maximum spell slot level of 5 (at the 9th level of warlock).
Do note that you can cast spells with slots that are higher level than the base spell. For example: hold person, a second level spell, can be cast with any spell slot of level 2 or higher. If you were to cast it with a higher level slot, it would even count as a spell of that higher level. Many spells even specify additional effects when you cast them at higher level, though not all do, and they don't need to have such a feature in order to be able to use a higher level slot.
In addition, the reason for the relatively limited number of slots is that warlocks regain their spell slots on a short rest as well as a long rest (unlike most other spellcasting classes).
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.
Best Answer
Yes this is correct...
Under the sections:
Spell Slots
PHB 107 (Emphasis mine)
It further describes an example:
So assuming you reach 20th level you will have 15 spells known, with 4 usable slots every short rest and all spells you cast will be cast as 5th level.
Spells Known of 1st Level and Higher
The slot levels indicate the highest level spells you know as well as the level at which you will cast the spell.
Mystic Arcanum are the higher "levels" of magic but they are treated somewhat differently as a balancing tool given how frequently a Warlock regains their slots.