Com tanto barulho, não consigo estudar.

Here com means with and introduces the cause or circumstance: with so much noise.

So:

• Com tanto barulho = With so much noise / Given so much noise
• It sets the scene before the main idea: não consigo estudar

In English, we might also say With all this noise, I can't study. Portuguese uses com in a very natural way for this kind of idea.

Because barulho here is being used as an uncountable noun, like noise in English.

• barulho = noise
• barulhos = noises / different sounds

In this sentence, the speaker means a lot of noise in general, so singular is the natural choice:

• tanto barulho = so much noise

If you were talking about separate noises, then plural could make sense in another context.

Both tanto and muito can refer to a large quantity, but they are used a bit differently.

Here, tanto often gives the sense of:

• so much
• that much
• a strong emphasis on quantity

So:

• Com tanto barulho = With so much noise

If you said com muito barulho, it would still be understandable, but com tanto barulho sounds more natural when stressing the amount and its effect on the speaker.

Because it agrees with barulho, which is:

• masculine
• singular

So the correct form is:

• tanto barulho

Compare:

• tanto barulho = so much noise
• tanta confusão = so much confusion
• tantos livros = so many books
• tantas pessoas = so many people

So tanto changes depending on the noun it goes with.

Here consigo comes from the verb conseguir, which means:

• to manage to
• to succeed in
• sometimes, in context, to be able to

So:

• não consigo estudar literally means I do not manage to study
• in natural English: I can't study

This is slightly different from simply saying não posso estudar.

• não consigo estudar = I can't manage to study / I’m unable to study
• não posso estudar = I can't study, often because I’m not allowed to or it isn’t possible for some external reason

In this sentence, conseguir is good because the noise is preventing the speaker from being able to focus.

Because não is the normal way to make a sentence negative in Portuguese.

• consigo estudar = I can/manage to study
• não consigo estudar = I can't manage to study

In Portuguese, não usually goes directly before the verb it negates.

Because after conseguir, Portuguese normally uses an infinitive to say what someone manages or fails to manage to do.

Structure:

• conseguir + infinitive

Examples:

• Consigo dormir. = I can/manage to sleep.
• Não consigo entender. = I can't understand.
• Não consigo estudar. = I can't study.

So estudar stays in the infinitive because it is the action linked to conseguir.

Yes, but it does not mean exactly the same thing.

• Não consigo estudar = I can't manage to study / I’m unable to study
• Não posso estudar = I can't study / I may not study

Não posso can suggest:

• lack of permission
• a rule
• an external obstacle
• physical impossibility

Não consigo focuses more on the speaker’s ability to carry out the action. In this sentence, because the problem is the noise, não consigo estudar is the more natural choice.

The comma separates the introductory phrase from the main clause.

• Com tanto barulho, = introductory circumstance
• não consigo estudar. = main statement

This is similar to English:

• With so much noise, I can't study.

The comma makes the sentence easier to read and sounds natural in writing.

Yes. Portuguese is fairly flexible here.

You could also say:

• Não consigo estudar com tanto barulho.

This is completely natural and probably even more common in everyday speech.

The difference is mostly one of emphasis:

• Com tanto barulho, não consigo estudar.
  Emphasises the noisy situation first.
• Não consigo estudar com tanto barulho.
  States the problem first, then gives the reason.

Both are correct.

Yes, it can be confusing for learners because consigo can be:

1. the 1st person singular of conseguir

   • eu consigo = I manage / I can

2. a completely different word meaning with you in more formal usage

   • consigo = with you

In this sentence, it is definitely the verb:

• não consigo estudar = I can't study

In European Portuguese, the verb form is pronounced roughly like kun-SEE-goo, though the exact sound is more reduced than in English and unstressed vowels are often weaker.

Yes, barulho is a very common everyday word in Portuguese. It can mean:

• noise
• loud sound
• disturbance

Examples:

• Há muito barulho aqui. = There is a lot of noise here.
• Que barulho é esse? = What noise is that?
• Os vizinhos fazem muito barulho. = The neighbours make a lot of noise.

So in your sentence, barulho refers to disturbing noise that makes studying difficult.

Yes, absolutely. It sounds natural and idiomatic in European Portuguese.

A speaker might use it in situations like:

• noisy neighbours
• traffic outside
• people talking loudly
• construction noise
• a loud TV or music

It is a very normal way to complain that the noise is making it impossible to study.