Re: making mad money and essentially having a mercenary standing army - as a doge of Venice ALONE I've been making 40-something gold a month after expenses. Now that I've cut my way through Germany northwards thanks to liberal application of Waldensian Holy Wars I make double that. With a 12k points' worth of retinues factored in the costs. Were I not too concerned about the bottom line, I could - and have - kept the largest (450 to recruit) mercenary groups on indefinite retainer when the reparations from a surrender were worth the added wait.
And I've essentially given up on upgrading trading posts since whenever I did get one at max upgrades, some douche or another would go and ruin it, making the upgrades cost more than they were worth - with smart post management you could likely get even more money.
Speaking of, I found it's a good idea to set yourself a baseline - 500 gold is nice in early game - as a republic. It gives you a nice reserve in case you need to raise some mercs or fight for election. Other rulers have an annoying Embargo CB which destroys all posts in the country if they win and other republics will be more than glad to ask the rulers to use it.
Agreed, I'm not sure I recommend upgrading trade republics at all. If you ever relax and lose an election, the Doge can decide to transfer some to another family... or himself. With a high enough stewardship or intrigue (or diplomacy?) you can nullify the event, but still. Trade post income isn't that important once you're at kingdom (most serene republic) level. Better to upgrade your manor and personal demesne.
Once you're strong, they're a useful tool for conquering other nations. I was able to set up trade posts in England from Mali (with a large distance modifier to the cost) then use the City Conquest CB which lets you claim a city if you hold a trade post in the county. IIRC I wasn't given the County Conquest CB which lets you conquer a county if you hold a city in it... Probably due to the long distance. But my troops were still able to mitigate attrition on these footholds, and I'm pretty sure it was counted as friendly for enabling looter status.
As an aside, I find it funny that your raiders who besiege one of your own occupied holdings... loot it. Liberates it too, but sets the portrait on fire and probably maluses the income, and gives you gold like any other raid. Makes a sort of sense, I guess.
I know I play pagan too much because I find myself looting border counties in a war, then doing a proper siege on the depleted holding with a proper force. By the time the massive New Administration bonuses wear off, the raiding will have worn off too... Might as well take what I can.
From what I've experienced, I would not be surprised if the highest speed is uncapped. I can only go to speed 5 if there is absolutely nothing going on, otherwise it is just too fast.
I can only handle speed 3, and only if I'm actively paying attention. I usually run speed 2 and use my laptop. It's a little annoying that, optimally, a new move order is required after almost every battle... But instead of pausing, the game throws up a massive obscuring summary.