Does the Journals have legal rights to suggest changing the affilation of the authors? The affilation of the University is correctly mentioned and legal under the University laws.
I think they can "suggest". A sole suggestion does not qualify as a prohibited act. The problem is when they make the publication conditional on a change of affiliation - here I would oppose.
As suggestion is concern they may suggest, if you have multiple affiliations. But they can't change or emphasis you to change it as an condition to accept your work.
That's a strange question-- of course not. However, the situation is not described. Possible reasons for intervention: 1) your affiliation with organizations that cannot be mentioned in this journal for insurmountable reasons; 2) a typo in the source; 3) an obscene title, etc.
Dear Nikola, of course no journal can suggest that you change your affiliation. All affiliations in the world are regulated by the state and the country's Ministry of Science. The best place to look is the Times Higher Education World University Rankings or the AD Scientific List, which contain a database of universities and an explanation of the rules.