I detected a tone of irritation/annoyance when she talks

  1. Applicant need to provide documentation proof of residency and work status. I asked, what kind of document do I need to provide for each segment/heading/requirement?
  2. I never know that the restaurant offer delivery services?
  3. You need to provide document to proof each of the segment such as residency and work status.
  4. I detected a tone of irritation/annoyance when she talks.

Are the above sentences correct?

  1. The applicant needs to provide documentation detailing proof of residency and work status.
    I asked, “what kind of document do I need to provide for each segment/heading/requirement?” – in reported speech that would be: I asked what kind of document I needed to provide for each heading/segment/requirement.
    The terms ‘heading’, ‘segment’ and ‘requirement’ are not familiar to me. This would not make sense in the UK.

  2. I never knew that the restaurant offered delivery services.

  3. You need to provide documents to prove each of the segments, such as residency and work status.
    Again, the term ‘segment’ seems strage to me. It seems perhaps you mean ‘sections’.

  4. I detected a tone of irritation/annoyance when she spoke.
    I detect a tone of irritation/annoyance when she talks/speaks.

Beeesneees,
“The applicant needs to provide documentation for proof of residency and work status.”
Is this sentence OK and meaningful?

‘for’ is not correct there. It indicates that documentation is required in order to get proof of residency and work status.
The applicant needs to provide documents which provide proof of residency and work status.
The applicant needs to provide documentation which proves residency and work status.