Chcę zaparkować samochód na parkingu obok apteki.

Polish verbs of wanting or intending—like chcieć, mieć zamiar, woleć—are followed by an infinitive.

• chcę (I want) + zaparkować (to park)
  A finite future form (zaparkuję) would stand alone, not attach to chcę.

zaparkować is perfective (completed action).

• Use zaparkować when you mean “to get the car parked” (emphasis on finishing the action).
  parkować is imperfective (ongoing or habitual action).
• parkować would stress the process (“to be parking” or “to park repeatedly”).

samochód is the direct object of zaparkować. In Polish:

• Verbs that act upon something take the accusative.
• Masculine inanimate nouns have the same form in nominative and accusative, so samochód stays unchanged but is still accusative.

The preposition na governs two cases:

• Accusative for motion onto something (e.g. jadę na parking “I’m driving onto the parking lot”).
• Locative for location (e.g. jestem na parkingu “I’m at the parking lot”).
  Here you’re describing where you want to park, so you use locative: parking→parkingu.

The preposition obok always takes the genitive.

• obok
  • apteka (nominative) → obok apteki (genitive)
    This construction means “next to the pharmacy.”

Yes, Polish word order is quite flexible. Both sound correct:

• na parkingu obok apteki (more common)
• obok apteki na parkingu (still understandable)
  Putting the more important or new information later can help with emphasis.

Yes, but with a nuance:

• przy
  • locative (aptece) means “by/at” and often implies immediate vicinity or association.
• obok
  • genitive (apteki) strictly means “beside” or “next to.”
    Depending on the context, both can be correct:
    • na parkingu przy aptece – at the parking lot by the pharmacy
    • na parkingu obok apteki – at the parking lot directly next to the pharmacy