Aside from selling ore, I noticed that I am given a seemingly random bonus at seemingly random intervals. Does anyone know how this is affected? And how frequently its actually supposed to happen?

Random bonus?
Maybe its your colonists taxes? :-) You know... more ppl you have, more money they pay.

Only one i noticed is third colony.

But i recall some one telling it was related to how much capital you had in structures. but that was decades ago on some forgotten forum.

Well, from time to time, game may decide that you need financial boost to improve your economy, reward you for colonizing previously inhabited asteroids (ie destroying other species colonies) and so on. Federation will even (under some circumstances - like no space dock and so on) send you new transport ship, if the original one was destroyed.
I never pinpointed precise rules, but thats only "random" financial bonus that I am aware of.

You wouldn't happen to know the rate would you? Like one credit per person?

No, sorry. Not sure about it. I'm not even sure about IF there is something like taxes. But i i can imagine that there is reason to have colonists on depleted asteroids.. other than mounting ast.engines and crash on enemy...

I do notice my money going up slowly even when I'm not mining so there is a trickle, but as far as what increments and how many is hard to tell due to the speed at which in game days elapse.

Though I haven't played FA yet and therefore don't know if there is something like an adjustable tax rate in FA, too...in the (spiritual) precessor Utopia it worked indeed that way that 1% tax equals 1 Credit, up to an maximum of 20% tax = 20 Credits per colonist and month. Maybe that formula was just kept...?

Recently i noticed that TetraCorp awarded me with reasonable amount of money, not sure for what but i did get message saying that.
Maybe they were more generaous in your game..

Tatracorp does give bonuses if you keep providing them with lots of minerals. I believe they also fine you if you're caught using the black market too much, but not sure on this.

As far as I've loosely come to understand, your pay may depend on your overall TetraCorp rating, but the issue with that, is that you cannot see your ranking until you've quit a session.