1) Sometimes they are required to prevent an AI from winning

. Other times they're just plain old fun

. Clearing your own continent is something I usually find easier. There are occasions however, where my neighbour has been even harder to kill than people on the other side of the world.
2) With really, really large armies in a lot of boats, don't stop building more units and reinforcing the invasion. The earliest era its really possible in is the Renaissance, during this period with just galleons it can be very difficult to get enough troops to the front to fight. A few frigates or ships of the line help a lot with breaking down cultural defenses. Try to hit the most productive enemy cities first, this is usually the capital (look for cities with many hills nearby, and cities with big populations). Hitting multiple cities on the first turn of invasion can totally cripple an AI don't be afraid to raze a few either, maintenance on overseas continence can build up fast!
Once you have flight it becomes incredibly easy, just rushbuy an airport in the first city you capture. You can only fly 1 unit per turn out of a city with an airport, but
you can fly as many units into a city with an airport as you have other cities with airports
.
Theres also the option to use fighters on carriers, these things are awesome. In fact the AI is so bad at stopping them I would argue they're overpowered in human hands. Use them in groups so you can have a lot of fighters hitting the same region, they work best if you use warships to break culture defenses, then attack the units in the city with your fighters to soften them up for your assault troops, also recon missions to find the enemy stack will help immensly. They're also kinda silly cos you can fly fighters into the carrier from anywhere in the world
3) Don't know of any unfortunately