This is an issue for the community to fix. @matthiasmullie to write a summary of what needs to be fixed and how, and @Keegan will post to the talk page.

(1)
These 2 were missing from the license map config:

	P275=Q98755364, # copyright licence = Commons Attribution-ShareAlike 3.0 Italy
	P275=Q98755344, # copyright licence = Commons Attribution-Share Alike 3.0 Serbia

I have added them, and the files in question now no longer appear in search results they don't belong.

We've intentionally made this license map something that the community can change, but IIRC we haven't really informed them about it. I will post more details about that in a separate comment.

(2)
This seems to be because there is less license information available from the API.
I've split this off into T273165 and added some more detail in there.

(3)
This file has a copyright license = attribution only license statement, so it think it's definitely not "no restrictions".
There may be another issue with where this specific license fits, however. I've split that off into T273166.

(4)
We currently only show icons for some (CC & PD) licenses.
It's be nice if we can show a generic fallback icon for the rest of the licenses. I've spit that off into T273167.

The map of these license statements can be found at https://commons.wikimedia.org/w/index.php?title=MediaWiki:Wikibasecirrus-license-mapping

It is the map of license names to structured data statements, for use with the haslicense keyword feature (or the Special:MediaSearch UI filter which uses the search keyword filter)
Changes to this take effect immediately.
The syntax is as follows:

• Everything from a "#" character to the end of the line is a comment.
• Every non-blank line is the license name, followed by a "|" character followed by a comma-separated list of <property>=<item> statements.

Examples of good lines:

cc-by-sa|P123=Q456,P123=Q789
cc-by|P123=Q000

Adding additional whitespace for improved legibility (e.g. newlines) is allowed around the | and , characters.
Example:

cc-by-sa|
    P123=Q456,
    P123=Q789,
cc-by|
    P123=Q000,

@Keegan: above is some documentation for how the community can update the license mapping, should the need to make changes. Can you make sure this finds its way to the relevant people?
Once that is done, you can close this ticket - the other things have been split off into separate tickets.