In my current game I'm having a problem with huge pirate fleets entering my territory and I can't seem to stop them. This isn't like Stellaris where you can hold choke points, the pirates just fly across deep space to hit some developing colony deep in my territory.

I know you can patrol, but the patrol Ai doesn't seem to be smart enough to cover an area and leaves their posts. Is there a way to actually protect my empire's borders?

There isn't really any way you can 'intercept' fleets in transit.
Well, not until you get right to the end of the energy tech tree anyway.

The best you can do for most of the game is use Long-Range scanners to see where the pirates are heading.

Building a resupply ship which is mostly made of fuel tanks and cargo bays with a scanner on top will give you a decent mobile platform so you can keep an eye on what the pirates are up to.
Just make sure to deploy it on a suitable gas giant for a while before sending it off so it can fill it's bays with fuel.
And try to keep it in space as much as possible - anything inside a system becomes a valid target for your opponent(s).

With any luck, you should be able to find the pirates, and the scanner will let you see which direction they're moving in so you can 'manually' trace that path to a potential destination, and send your fleets there to wait for them.

Oh, using resupply ships as mobile scanners is an idea. I've been putting them on my ports and made a dedicated starbase for surveillance, and when you want to put a port over every colony (to increase trade and give med and rec benefits) it can get pricey.

Is there a way to control what ports can build what? I'm used to stellaris where you can use starbases to repair ships without having to put shipyards on them, but in distant worlds it seems that you need construction yards to repair? Which means that when you want to build a fleet the new ships are scattered across the empire and it takes so long for them to get assembled.

I just want to have military ship production to be handled by a few spaceports and let the rest build either civ ships or repair patrol fleets.

Also, what do I have to do to make a foreign colony defect? The Shandaran / gekko people have a colony near my core worlds which is a pretty inconvenient spot, and I've been trying to use covert ops to cause rebellions but their happiness drops to 0 and then goes back up to 16 in like a second. Is there a way to actually make the rebellion happen?

Scanners on ports is always good imo. Easy to have enough energy collectors to run them.
Monitoring stations are also good, but are a bit limited as they can't move. You can build them in deep space though, if you zoom in close enough with a constructor selected and right-click "build here".
I like to put scanner stations next to fuel mines - not nescessarily all of them, just so they roughly cover an area.

You can manually control which ships are built where by selecting the port you want and using the build options from either the bottom of the UI display panel or the right-click menu to queue up individual ships.

This is quite tedious though. I tend to only do this to build a single fleet at a location, and use the build planner only for generating automated patrol ships (which never get put in fleets and just roam around on thier own).
If I ever want an automated patrol fleet, I will grab whatever ships are in a specific area, fleet them up and send them on thier way.
There's no real rules for this - do whatever works for you.

I don't think foreign colonies ever defect.
The only way to make a foreign power colony yours (that I know of) is to invade it with troops and take it over.
You can make the colony rebel via spying etc, and this has a small chance to make it leave it's current empire.
At which point it becomes an independant colony, and can be either invaded or have a colony ship attempt to land on it.
(Shandar get some happiness bonuses, so it might be difficult to make them unhappy enough to leave thier current empire.)

I don't think there's even any diplomacy options for trading colonies.

Thank you for your advice. I finally managed to beat the game on normal with Shakturi.
Funnily enough, I didn't win by beating the Shakturi; I won a standard victory about 1 minute after the Shakturi revealed themselves.

I continued playing for a bit to see if I can beat them this time and I stopped after taking their homeworld because...well, the game's war system isn't very good and Shakturi ships are a slog to fight, even if you're winning so I just stopped there.

I'm not sure if the Shakturi were ever play tested; they feel like they need a lot of meta knowledge to beat, as I only really managed to take their home world by building the Planetary Fortress first and deny them the +200% defensive boost and aggressively used spies to steal their tech. Even then their ships seem to cheat on stats? They somehow manage to keep them low size and yet with 1k firepower, lots of shields and speed.
When I try to do that on one of my cruisers it's way more than 700 size and nowhere near as fast.

I guess I could have just disabled the Shakturi the whole time and beat the game earlier, but I only found out about that option during the latest attempt and I wanted to see if I can fight them this time. I can now, I know I can and I don't want to because they are boring.

Congrats on beating the game!

I agree about the Shakturi. They feel like they're the result of a very heavy-handed approach to difficulty that I don't really like all that much.
Fortunately they're optional.

Hopefully you can find some settings and goals that will provide a more enjoyable experience.