How do I attach a source from the "All Collections Search"?
The same way as if you'd found it by some other method?
The search results in the "All Collections Search" do not have the same slide out side panel for evaluating and attaching sources as does the regular Search section. I have no idea if this has just not been added yet or if it is because so many of the results are not attachable sources so it was felt best to leave that feature off.
For Historical Records results, click on the document icon and it will take you to the record so that you can evaluate it. There is an Attach to Family Tree button on that page if the source is not already attached to someone. If it is, it shows you who the record is attached to.
Family Tree profiles are not sources and cannot be attached.
Memories are not sources and cannot be attached.
Last name information is not a source and cannot be attached.
Genealogies can have sources but often are just poor quality repetitions of what is in Family Tree. They should not be attached as sources but only used to lead you to sources.
Catalog and Books again may lead you to sources but are not in and of themselves sources.
Image Only Records is just a link to take you to that part of the website and does not take anything from your search with it. I would wonder if there are future plans to add an initial search for a place if specified in the original search.