You can trade with other factions if your're allied/neutral with them, otherwise no. If enemy ships are in sea zones along your trade routes, that will blockade your trade (and you theirs)
Adding a port does nothing for your trade, you need a trading post of some sort. If memory serves, this allows you to trade your goods with other factions and get the import tax from others trading with you (for the latter, if the other faction moves their ships around/gets blockaded, the import tax may disappear for a year or two and come back).
Not necessarily, but by having more ships in more seas adjacent to ports with traders you are trading with more provinces. You cannot trade goods which the province already has however.
There are too many factors to list. Your governors may have picked up some vices, if you train more troops that's higher support costs, if you're at war your trade routes may have been blockaded, etc, etc. Ship support is also a factor. This is why the med islands are desirable, they give a home port to ships which are far from your homelands (ship support increases as ships get further from home). Taxes are another factor, but assuming you're not using auto taxes then you should be in control of these and able to factor in.
Not really, all an inquisition does is raise zeal to a very high level before the inquisitors go berserk, then zeal drops again drastically. This makes inquisitors zeal raising capabilities a double edged sword. The only economic effects would be if an inquisitor took it upon himself to try one of your governors - thus leaving the province ungoverned and bereft of the additional income bonuses which his governorship produces (high acumen increases tax income/productivity).
No. If you're still allied to the papal faction and not at war, then this should not be a factor - though if the papal assassins/inquisitors kill your governors... (see above).
The random factor is mostly due to V&Vs and natural disasters.
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