Welcome to the forums and Civ IV

. In general I'd suggest reading through some of the shadow games on this forum and watching a few of Lain's videos, just to get a general idea of how things like diplomacy works, what options you've got, etc. Don't expect to pull crazy Deity-level stunts immediately, but knowing everything that Opens Borders does would be a good starting point. As for your specific questions:
1. No, that's not an efficient strategy. The benefit of founding a religion is that you've got guaranteed access to a religion (this only really matter is games where you're isolated until Astronomy or when you're playing something like Always War, otherwise AIs will happily found/spread their religion to you), a holy city generates I
believe +5

per turn as opposed to the +1

per turn that just a religion spread generates, and a Great Prophet can build a Shrine of any religion in that religion's holy city. Keep in mind, none of those are really worth going out of your way for yourself, especially on higher difficulties. If you happen to found, say, Confu or Taoism, no harm done, but delaying worker tech to go Meditation or Poly at the start of the game can really slow down you down.
As for adopting a religion, everyone who also runs that religion will get a positive diplo modifier, and everyone who runs a different religion gets a negative diplo modifier (exactly how much depends on the AI in question - someone like Saladin gives a large bonus/penalty, whereas Stalin won't care very much either which way). Every city that has that religion present will get +1

for having your state religion present in the city. If you're running the AP religion your votes count double, and you qualify for being voted as the AP Resident if you've got more population than your competition. Most importantly, several bonuses given by Religious civics only work if your state religion is present within a city - Organised Religion's +25%

bonus on buildings, Theocracy's +2xp on every unit build in a city, and Pacifism's +100%

generation all don't work if you don't have your state religion present within a city, or if you're not running a state religion in the first place.
Generally the better strategy is to open borders with everyone, both to start building relationships and to improve your trade routes, as well as letting the AIs spread their religion to you. It slows them down without really hurting you at all, and in fact if you want to run something like Pacifism later it's really helpful to have AIs spread a religion to all of your cities basically for free. Otherwise you'd have to spend a lot of hammers on Monasteries and Missionaries. In addition, if a situation pops up where a very large portion of the map is running the same religion you can easily adopt it yourself and enjoy a host of diplo bonuses for relatively no penalty.
2. It depends on the map, really. There's situations where you
really want Great People so you'll be running specialists anyway, there's situations where they're just not enough good tiles for cottages or enough food to run specialists, is depends. I will say that if you build the Pyramids and run Rep, focus on farms. Maybe cottage your capitol anyway, to take advantage of the Bureau bonus later, but otherwise, farms. Rep scientists are much better than growing cottages, in
most situations of course.
3. Tech advantage, and siege. If you're using pre-Gunpowder units, Walls and later Castles really make it hard, if not impossible, to take a city with attackers alone. Bring along siege to bombard down defences, throw them into the city to weaken the defenders, and then send in your attackers to clean up. You'll lose some catapults/trebs throwing them against the defenders, but those are expected losses. Gunpowder units, which ignore walls/castles, can punch through defenders the hard way
if you're at a tech advantage. Cuirassier can punch through longbows/pikes and Cavalry can punch through muskets, if you've got enough of them. Rifles will stop either of them dead in their tracks, however. If you're at a tech parity, use siege.