If you park a fleet in a port, you don't need to patrol the local area, so one ship can cover 3-5 coastal provinces. I wasn't aware that fleet size increased the safe zone radius, I was under the impression that it had something to do with tech level, because it seemed to increase over time, but bigger fleets would also occur over time.
Active patrols keep pirates from spawning for 30 days in the patrolled provinces ONLY, so a larger active patrol group does nothing, until pirates spawn (then you've got more ships to fight them). Patrols in port have an effect radius, safeguarding nearby sea provinces in addition to their own.
I normally move fleets directly from port to port, so they get more opportunities to repair. Repairs are always done on the first of the month, so if you dock the ship on the last day of the month, you only need to sit in port for a day or two. As long as you remain in supply range and in a coastal province, you should take no Attrition.
Starting more colonies than you can afford is a bad idea. Finish one ASAP, to help get back within your budget. In most games, I've got 2-4 going at a time; any more than that takes too much money away from other things, any less and I'm not getting much of an advantage from the natural growth rate of the colonies themselves. Normally, I try to send colonists to the province with the lowest natural growth rate (usually due to hostile natives, except in Tropical provinces where there's a penalty), and let those with the highest growth rates develop on their own. If there are passive natives, they'll add population to the colony when it completes; hostile natives are far more likely to attack your colonists. I usually sent troops to wipe out a few of the most violent tribes, while assimilating the more passive ones. The native tribes will gain a few tech levels fairly quickly, but won't catch up. You should be able to retain a massive technological edge through the end of the game. I had colonies adjacent to the native Americans by 1500 in my current campaign, and still have not wiped out the last of the natives by 1630. I'm at Land tech 27, they're up to around 6. They're in a different tech group, so the neighbor bonus isn't that high.
The Danish Sound Toll is something you'll need to decide for yourself: can you take on Denmark and whatever allies and vassals it has, and end the toll, or will that end up costing you more than the tolls? I assume that Japan won't open its markets without a war.
If you've got two coastal CoTs, I'd keep both for the bonuses. If one's an inland CoT, you might consider deleting it, but if that makes the other too profitable, someone else will open up a competing CoT of their own. I occasionally delete inland CoTs that I capture, then open coastal CoTs to replace them.
The cost for additional special buildings increases, but the costs seems to depend on some unknown factors. I've bought them for 900-ish ducats, built another for about the same cost, and then the next one cost over 1400. If I start building another right away, the cost is even higher, but if I wait until the previous one is completed, the increase seems to be lower, or it's the same price as last time. No idea how the cost is figured, whether it's based on the percentage of your provinces with them, tech level based, or there's some time delay before you can build another without raising the price. I'm up to somewhere around 12-14 such buildings, nearly half of them Universities from annexed provinces. There are factories, where you can build one per province, and then there are unique buildings that you can only construct one of in your empire, once you've reached the tech level to unlock them.