No quiero usar dinero prestado para pagar la multa.

In Spanish, querer + infinitive takes the infinitive directly: quiero usar, quiero pagar, quiero ir.
You don’t add a the way you might in some other structures. (You can see ir a + infinitive: voy a usar, but that’s a different verb pattern.)

Yes, No quiero usar... is the normal placement: no goes right before the conjugated verb (quiero).
You generally don’t put no right before the infinitive here (so Quiero no usar... sounds like “I want to not use...” and shifts emphasis).

Dinero prestado means borrowed money and doesn’t require you to say who lent it.
If you want to add the lender, you can:

• dinero prestado por mi hermano = money borrowed from my brother (literally, “lent by my brother”)
• dinero prestado de mi hermano can be heard in some places, but por is often clearer for “lent by.”

Prestado is an adjective meaning “borrowed,” and it agrees with dinero (masculine singular).
Examples of agreement:

• dinero prestado (m. sing.)
• plata prestada (f. sing.; common in Latin America)
• fondos prestados (m. plural)
• sumas prestadas (f. plural)

Yes, and it slightly changes the focus:

• No quiero usar dinero prestado... = I don’t want to use borrowed money (maybe you already have access to it, but don’t want to use it).
• No quiero pedir dinero prestado... = I don’t want to borrow money / ask for a loan in the first place.

Para + infinitive expresses purpose: in order to pay.
Por + infinitive usually expresses cause/reason or “for doing” something, depending on context, and would not fit the “purpose” meaning as cleanly here.

Not in this meaning. a + infinitive can appear with certain verbs and expressions (like ir a pagar, ayudar a pagar), but it doesn’t generally mean “in order to.”
For purpose, para pagar is the natural choice.

La multa often implies a specific, known fine—either already mentioned or obvious from context (“the fine I got”).
Una multa would be more like “a fine” in general or an unspecified fine.

Multa is widely understood and standard for “fine.”
Depending on country and context, you may also hear:

• infracción = the infraction/violation (sometimes used for the citation itself)
• comparendo (e.g., Colombia) = ticket/citation
• boleta (some countries) = ticket
  But pagar la multa is broadly safe across Latin America.

You can, but the meaning changes.

• No quiero usar dinero prestado... = I don’t want to use borrowed money.
• No quiero dinero prestado... = I don’t want borrowed money (I don’t want to receive it / I don’t want that option).
  Keeping usar makes the “use” idea explicit.

Here you want pagar because you are paying something: pagar la multa.
Pagarse is reflexive and is used differently, for example:

• Se paga con tarjeta = It’s paid with a card / You pay with a card (general statement)
• La multa se paga en el banco = The fine is paid at the bank (passive/impersonal)
  But your sentence is a personal statement, so pagar fits.

Common options:

• No quiero usar dinero prestado para pagar la multa. (neutral)
• No quiero usar dinero prestado ni para pagar la multa. (not even to pay the fine)
• De verdad / En serio no quiero usar dinero prestado... (I really/seriously don’t want to...)
• No quiero para nada usar dinero prestado... (not at all)

Both are common in Latin America.

• dinero is neutral and works everywhere.
• plata is very common and informal in many countries.
  So you could also say: No quiero usar plata prestada para pagar la multa.