I just realized the bibliography insertion bug seems to stem from the fact that the section numbering is broken: since I'm missing section 2 after deleting one section and the subsequent sections not updating the bibliography gets inserted at this point in the document.
The bibliography is simply a section that's in a certain position in the document – it can be moved in the outline as well. Regarding the section numbering, I'm not 100% sure I understand correctly the problem, would you mind sending us the document in question via firstname.lastname@example.org and refer to this forum post there, please?
On a different note, is there any way to control the order of references (in the text, not the bibliography) and what order do they currently follow (seems to be neither alphabetical nor chronological)?
That depends on the citation style. Sending us an example via email@example.com where you feel something confusing is happening is the best way to help us assist.
And is there any way to output the bibliography again if you deleted it once but still have the citations inserted in the text (hitting bibliography will only create empty bibliography although I have references in the document)?
Yes, absolutely. Simply use Insert > Bibliography to insert a bibliography section. That will then collate the citations in the document.
CEO & Co-founder of Manuscripts.app Ltd