A volte non chiedo il permesso perché penso di dare fastidio, ma poi capisco che sbaglio.

Yes. A volte means sometimes or at times.

• a = at / to
• volte = times

So A volte is a fixed expression meaning sometimes. Italian commonly uses it without an article, unlike English phrases such as at times.

Italian usually drops subject pronouns when they are not needed, because the verb ending already shows the subject.

• chiedo = I ask
• non chiedo = I do not ask

The pronoun io can be added for emphasis, contrast, or clarity, but it is not necessary here.

Chiedo is the first person singular present indicative of chiedere.

So:

• chiedo = I ask
• non chiedo = I don’t ask

Italian often uses the present tense for things that happen habitually or generally, just like English does in sentences such as Sometimes I don’t ask permission.

Yes. Chiedere il permesso is a very common Italian expression meaning to ask for permission.

Literally, it is to ask the permission, but in natural English we usually say ask for permission or ask permission.

Examples:

• Chiedo il permesso di uscire. = I ask for permission to leave.
• Hai chiesto il permesso? = Did you ask for permission?

So this is standard Italian.

The accent marks the stressed final vowel and distinguishes the word correctly in writing.

Here perché means because.

Italian writes this word with an acute accent on the final é:

• perché

This is the normal spelling whether it means because or why, depending on the sentence.

After pensare, Italian can use two different patterns, depending on the meaning.

1. pensare di + infinitive
   This is used when the subject of both verbs is the same.

   • Penso di partire. = I’m thinking of leaving / I think I will leave.
   • Penso di dare fastidio. = I think I’m bothering people / I think I might be a nuisance.

2. pensare che + finite verb
   This is used more for thinking that...

   • Penso che lui abbia ragione. = I think that he is right.

In your sentence, the subject is the same throughout: I think I am bothering. So penso di dare fastidio is the natural structure.

Dare fastidio is an idiomatic expression meaning:

• to bother
• to annoy
• to be a nuisance
• to disturb

Literally, it is to give annoyance/discomfort, but you should learn it as a set phrase.

Examples:

• Ti do fastidio? = Am I bothering you?
• Non voglio dare fastidio. = I don’t want to bother anyone.

In this sentence, penso di dare fastidio means I think I’m bothering people or I think I’m being a nuisance.

Italian often leaves this unstated when it is understood from context.

• dare fastidio can appear with an indirect object:
  • Ti do fastidio? = Am I bothering you?
• But it can also stand alone:
  • Non voglio dare fastidio. = I don’t want to bother anyone.

So in your sentence, the person or people bothered are implied rather than named.

Ma means but, and poi here means then, afterward, or later.

So:

• ma poi = but then / but afterward

It shows a contrast:

• first: I don’t ask permission because I think I’m bothering people
• then: later I realize I’m wrong

Capisco means I understand / I realize.
Che introduces a clause: that.
Sbaglio means I am wrong or literally I make a mistake.

So:

• capisco che sbaglio = I realize that I am wrong

This is a very natural Italian structure.

Both exist, but they are used a little differently.

• sbagliare = to make a mistake, to be mistaken
• sbagliarsi = to be mistaken

In many contexts, sbaglio works perfectly well to mean I’m wrong:

• Capisco che sbaglio. = I realize that I’m wrong.

You could also hear:

• Capisco che mi sbaglio.

But capisco che sbaglio sounds direct and natural.

Yes, Italian word order is fairly flexible, but this version is the most neutral and natural.

Current structure:

• A volte = time expression
• non chiedo il permesso = main clause
• perché penso di dare fastidio = reason
• ma poi capisco che sbaglio = contrasting result

You could move parts around for emphasis, for example:

• Non chiedo il permesso, a volte, perché penso di dare fastidio.

But the original sentence sounds smoother and more natural in everyday Italian.

It is neutral, natural Italian. It is not especially formal or especially casual.

The vocabulary is everyday:

• chiedere il permesso
• dare fastidio
• capire
• sbagliare

So it would fit normal conversation, writing, or personal reflection.

Not really. In this sentence, poi is closer to:

• then
• afterward
• later

So ma poi capisco che sbaglio means but then/later I realize I’m wrong.

Eventually in English often suggests after a long time, which poi does not necessarily imply.

Yes. Very often it is followed by di + infinitive to say what permission is being requested for.

Examples:

• Chiedo il permesso di entrare. = I ask permission to come in.
• Hai chiesto il permesso di uscire? = Did you ask permission to go out?

In your sentence, the speaker simply says I don’t ask permission, without specifying permission to do what.