The rules for Basic Spellcasting state:
Basic Spellcasting Feat: Available at 4th level, these feats grant a 1st-level spell slot. At 6th level, they grant you a 2nd-level spell slot. At 8th level, they grant you a 3rd-level spell slot. Archetypes refer to these benefits as the “basic spellcasting benefits.”
If you take this feat at 4th level, do you have to take it again at 6th level in order to get the 2nd-level spell slot? Or do you just automatically get it and you are free to choose another feat at 6th level? (I don't know if it is even possible to take feats more than once.)
Furthermore, what if you want to delay your multiclassing, and you dont take Basic Spellcasting until level 6. Do you get a 1st-level or a 2nd-level spell slot? Or both?
This whole wording is very unclear to me.
Each Feat (Basic, Expert, and Master) (Class) Spellcasting provides all its spell slots at the appropriate character levels.
You get the full benefit based on character level, regardless of when you take the Feat. In your example of taking the Feat at level 6, you would gain both the 1st and 2nd level spell slot.
Firstly, there is no other "level" in Pathfinder v2 that this could refer to. With their assimilation of Multiclassing and Archetypes into your character level, you only have one level that it could be referring to.
Second, you may only take the Feat once unless it says otherwise (it does not). For example, the Basic Bard Spellcasting Feat (page 222)
Third, looking at the above quote, it assumes you gain new spell slots while having the Feat "Each time you gain a spell slot of a new level from the bard archetype..."