At the higher difficulties, I've found that the only way to win is to play defensively. Siege units, at least one in each city, probably flanked with another siege unit (or two on a border with an aggressive enemy) and some front line infantry is really the only protection.
My second city is almost always founded in an area with a lot of production bonuses (hills, iron, stone/marble, horses/cows/sheep, etc) and focuses completely on producing military for the entire game. If you grow large enough, founding an additional city of this type can be useful, but if you've got around half a dozen cities or less, one is generally sufficient. Have this city crank out units and only build military buildings there (ideally by rushing them, if you've got the cash). Most of the rest of the empire is money- and happiness- focused, although they might churn out disposable units if war is looking inevitable or going poorly.
When it comes to science, pick techs that get you closer to:
- Money production buildings, like the Bank
- Better siege units (trebuchet, cannon, and especially artillery)
- Better front line infantry (musketmen, infantry, mech. inf., etc)
The AI will become increasingly aggressive towards you if they feel your military power is less than theirs. However, they're terrible military strategists. They will send their entire army right to your cities, with no regards to how that leaves their defenses or how positioning effects their chances at survival. At the higher levels of difficulty, this can mean an almost constant trickle of units.
However, they tend to fail to prepare for the bonuses you gain for fighting on your own turf - take these whenever possible, and then turtle heavily when they declare war. After a while, you'll have an army of extremely powerful units (ie, 2-shot per turn siege units with extra combat range, etc) and great generals, which you can use to push the tide back. Plan on cranking out front line infantry units, as they're somewhat disposable. Put a large priority on preserving your high-level siege units, though.
Likewise, if you see a weak neighbor, go after their stuff. The AI gets big bonuses to production, so their cities are going to be better equipped than ones you could found yourself. Declare war, turtle for a few turns while they bumble about ineffectually at your borders, and then steamroll.
Just remember not to completely abandon your own defenses...
Best Answer
Station an inquisitor/inquisitors in your city/cities and he will be unable to act. Alternatively you should be able to surround the city with 6 workers/other non-combats (triangle units) and he won't be able to get close enough to use his ability.
If he does successfully convert some citizens, you can use an inquisitor to remove his influence, but its preferable to block him by just stationing the inquisitor there.
I don't believe any of those will cause a diplomatic hit. If one of them does, it would be using the inquisitor to remove influence after the GP is used on a city.