Organise Document Libraries by projects or departments or both?

Question

We have various departments that may have various managers that can initiate projects from clients. (Not always the same department everytime.) We have subsites for every department and (very likely) subsites for every project.
I'd like to see a document library per department. Every document metadata shall have an associated project number. On the project page, I'd like to see a single view of documents from various libraries that have the corresponding project number.
Is this doable?

Answer 1

Yes, it is.
The easiest way is to build a template site, with the document library including the relevant metadata, and then save it as a template ('Project Site Template'). You can then create new sites using that template which will create a new copy of that document
library.
The second bit is about the default metadata for the column. This article is for 2010 but should be valid for SharePoint online.
https://msdn.microsoft.com/en-us/library/office/ee557925(v=office.14).aspx
To amalgamate the content you can use the Content By Search Web Part which will look at all items the user has permission to see (not real time but it does update regularly)
https://support.office.microsoft.com/en-gb/article/Configure-a-Content-Search-Web-Part-in-SharePoint-0dc16de1-dbe4-462b-babb-bf8338c36c9a?CorrelationId=df19aeb8-9693-4d16-85ce-f161e969b2f4&ui=en-US&rs=en-GB&ad=GB