Tercüme - Brezilya Portekizcesi-İngilizce - lu desculpe pela demora eu estava ocupada .......

maybe he is trying to say "my infinate particulars" which would be correct in English/

Dramati, I don't think so... I don't know exactly what's his intention, what he actually wanna say, but I bet it's not what you mean.
Anyway, I decided to translate literally what's written in the second setence.

yes, I understand what you are saying, however, the literal word for word translation has no meaning in English so I won't be able to validate it until you find some English phrase which will be acceptable.

Does 'particular infinite' fit better?

Could you explain what's the problem here please? the page has been checked.

The problem is the term "my particular infinite".

It is meaningless in English and we need to find something that might fit.

Would "personal infinite" make sense in English?
or "particular world"? or "particular skyline?

I agree with David. The correct meaning is:

"my infinite particulars". It means the too many things I have to deal with in private life (and keep me busy).

So lets make it my infinite particulars.