I read earlier that orbital installations are system-wide so they affect all stations? Is this still a valid thing?
Mostly, yes.
The effects on system variables are system wide
The pre-requisite enabling for other constructions is system wide
The effects on station services may be system-wide or may be localised to the body they orbit (more often system-wide)
The economic influence is local to the body as a strong link, and system-wide as a weak link (see below for more on what that means)
I'm also curious of other installations such as agri or mining? Does that mean if my outpost is orbiting a non-landable body adding such installation should enable certain wares like foods or mined resources?
Or indeed if it's orbiting a landable body. If an installation has an economic influence listed, it will create a strong economic link to a station orbiting that body, which will add an amount of economy of that type (between 0.1 and 1.2 strength, depending on the installation and the context of the system and body it orbits) to the station. It will also create weak links to stations orbiting other bodies (these are always strength 0.05) which will affect their markets too - though not as much.
This isn't as simple as "adds foods" - it makes the economy more agricultural (say), which increases the likelihood that agricultural exports such as food, drugs, fabrics, etc. are exported, and increases the likelihood that agricultural imports such as many forms of machinery, manufactured product, technology, etc. are imported. So if your station was previously an industrial station, you might find that it stops exporting Crop Harvesters and starts importing them (if not, the amount of Crop Harvesters it exports will almost certainly still fall somewhat relative to the other things it exports)
The exact outcome of this is very difficult to predict with certainty, so if you're in any way picky about what your stations import or export it's best to try to keep them to a single economy type as far as possible until you have a much better understanding of how Elite Dangerous constructs station economies.
What does Govt installation do?
Provides a moderately cheap way to improve system security, standard of living and development level without altering the economic balance of the system in any direction. That "without altering" bit is potentially very useful if you have your station economies set up how you want them, and just want to make the system more secure and productive overall.