Gracias por la ayuda.

Because por is the preposition normally used after gracias to mean for.

• Gracias por la ayuda = Thanks for the help
• Gracias por venir = Thanks for coming
• Gracias por todo = Thanks for everything

Using para here would sound unnatural. In this pattern, just remember:

• gracias por + noun
• gracias por + infinitive

In Spanish, nouns usually need an article more often than in English. So la ayuda is the natural way to say the help in this sentence.

• Natural: Gracias por la ayuda
• Unnatural in most cases: Gracias por ayuda

Spanish often uses the definite article where English does not, especially with general or understood things.

Yes. In Gracias por la ayuda, ayuda is a noun, meaning help.

Here is the difference:

• la ayuda = the help → noun
• ayuda as a verb form can mean he/she helps or help! in other contexts

In this sentence, the article la makes it clear that ayuda is a noun.

Yes. It is polite and natural in both formal and informal situations.

You can say it to:

• a friend
• a coworker
• a stranger
• customer service
• a teacher

If you want to sound a little more specific or formal, you can also say:

• Gracias por tu ayuda = Thanks for your help
• Gracias por su ayuda = Thank you for your help (formal)

Both are correct, but the nuance is a little different.

• Gracias por la ayuda = Thanks for the help
  
  • focuses on the help itself
  • slightly more general
• Gracias por tu ayuda = Thanks for your help
  
  • directly mentions that the help was yours
  • feels a bit more personal

Similarly:

• Gracias por su ayuda is the formal version

Because Spanish, like English, often uses short fixed expressions without a full verb.

• Gracias por la ayuda literally looks like Thanks for the help
• You do not need to say a full sentence like I give you thanks for the help

It is a complete, natural expression on its own.

Grammatically, gracias is plural in form, but learners usually just treat it as the fixed word for thanks or thank you.

That is why you see expressions like:

• Muchas gracias = Many thanks
• Mil gracias = A thousand thanks

You normally would not use gracia by itself to mean thanks.

Yes, absolutely. That is very common.

Some natural variations are:

• Gracias por la ayuda = Thanks for the help
• Muchas gracias por la ayuda = Thanks a lot for the help
• Mil gracias por la ayuda = A thousand thanks for the help

These all sound natural in Latin American Spanish.

Yes. After gracias por, you can use either a noun or an infinitive.

Examples:

• Gracias por la ayuda = noun
• Gracias por venir = infinitive
• Gracias por esperar = infinitive
• Gracias por todo = noun phrase

So this pattern is very useful:

• Gracias por + thing
• Gracias por + action

A simple pronunciation guide is:

GRAH-syahs por lah ah-YOO-dah

A few helpful notes:

• gracias usually sounds like GRAH-syahs in most of Latin America
• por has a short tapped r
• ayuda is stressed on yu: a-YU-da

If you want to sound more natural, say it smoothly as one phrase: GRAH-syahs por lah ah-YOO-dah

Yes, but it means something slightly different.

• Gracias por la ayuda = Thanks for the help
• Gracias por ayudarme = Thanks for helping me

The first focuses on the help as a thing.
The second focuses on the action of helping.

Both are natural, and sometimes they are almost interchangeable depending on context.

Yes. Gracias por la ayuda is completely natural in Latin America.

You may also hear very common alternatives such as:

• Gracias por tu ayuda
• Muchas gracias por la ayuda
• Gracias por ayudarme
• Te agradezco la ayuda in some contexts

But Gracias por la ayuda itself is standard and widely understood everywhere in the Spanish-speaking world.