Are there any standardized requirements for applying for a Schengen visa in a country, where you aren't a citizen nor permanent resident?
I don't think there is. There is a general principle laid out in article 6 of the Schengen Visa Code:
Consular territorial competence
- An application shall be examined and decided on by the consulate of the competent Member State in whose jurisdiction the applicant legally resides.
- A consulate of the competent Member State shall examine and decide on an application lodged by a third-country national legally present but not residing in its jurisdiction, if the applicant has provided justification for lodging the application at that consulate.
But how this is checked and enforced is up to each consulate, as far as I know. It will in particular depend not only on the Schengen country you are applying to but on the third country where you are applying from. Each consulate has to define rules based on the type of visas, permit, etc. local residents have.
What counts as “justification” (to waive the requirement per the second point above), I don't know either.