The Warlock list confuses me. It says that you have spell slots but not the spell slot level and at level 20 you only get 4 spell slots? Is this right? Also it says slot level. I'm guessing that's for what level of spell you can pick at that level. Am I correct with that as well?
Yes this is correct...
Under the sections:
PHB 107 (Emphasis mine)
The Warlock table shows how many spell slots you have. The table also shows what the level of those slots is; all of your spell slots are the same level.
It further describes an example:
For example, when you are 5th level, you have two 3rd-level spell slots. To cast the 1st-level spell thunderwave, you must spend one of those slots, and you cast it as a 3rd-level spell.
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.
A spell you choose must be of a level no higher than what’s shown in the table's Slot Level column for your level. When you reach 6th level, for example, you learn a new warlock spell, which can be 1st, 2nd, or 3rd level.
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.