What is the ethical way of writing co-author names?
You might have to check with your journal guidelines. Here are some examples:
Elsevier

Four criteria must all be met to be credited
as an author:

Substantial contribution to the study
conception and design, data acquisition,
analysis, and interpretation.
Drafting or revising the article for
intellectual content.
Approval of the final version.
Agreement to be accountable for all
aspects of the work related to the
accuracy or integrity of any part of
the work.

[...]
Three types of authorship are considered
unacceptable:

‘Ghost’ authors, who contribute
substantially but are not acknowledged
(often paid by commercial sponsors);
‘Guest’ authors, who make no
discernible contributions, but are
listed to help increase the chances of
publication;
‘Gift’ authors, whose contribution is
based solely on a tenuous affiliation with
a study.


Springer
Has nearly the same principles.
Your university
Likely your university has a document where they spell out the guidelines. The ethics department, if it exists, shall answer all of your questions.
Your specific questions (my opinion)

If a person help you to collect some amount of data (not all), either giving you permission or participated himself to help you in data collection - Yes (although I'm not sure what you mean by the &quot;giving you permission&quot; part)
Proofread the paper once or twice - I'd say no. Correcting typos is not a major scientific contribution.
Supervised you or co-supervised you but did not work in paper writing nor reviewing because of time constraints - If supervised means giving guidance and participating in discussions, yes. If supervised means just overlooking the progress of the paper without substantial input, then no.
The head of departments or labs - Just being the head of lab does not suffice. The authors contribute to the project directly.
The one[s] who support you financially. - These are typically credited in the acknowledgment section, not by giving them authorship.

Acknowledgments, on the other hand, are less strict. So even minor contributions, conversations or comments on the draft might be sufficient for putting someone in the acknowledgments.

Note: In this answer I'm not saying anything about the order of the authors because it's field dependent and I have no experience about it (my field being one that adopts alphabetical order).