Set your Warrior to auto-explore. He'll uncover the whole map while you think of clever strategies based on the terrain that you're given.
Bad idea. You want your Warrior for early barb rushes. He can do some exploring before, say, turn 25. But after that he needs to go hi-tail it to your capital and protect your tiles (especially if you went for an early worker and have upgraded tiles).
Automate is ok once you've basically won the game anyway, but the early game is the WORST time for automated anything.
If you have peaceful inner intentions the AI won't declare war on you. There's no need to build units.
Depends on your neighbors and if you do anything to tick them off. Settling near your neighbors ticks them off. Being more powerful (in population, cities, or whatever) ticks them off. They also are more likely to invade if your army is wimpy. You can't really spam units early on, but you'll want a few to deter the Shaka's and Alex's of the world. Its sort of like outrunning a bear - you don't have to more units than the bear, you just have to be a harder target than the other guy.
Opening Honor enables your scouting Warrior to better tackle the barbarian scum. Always take the opener at the very least.
THe honor opener has its place, however it isn't ALWAYS the first move you want. If you're planning on attacking (relatively) early, like when you're playing Zulus or Assyrians, Honor (the whole tree) might be useful. Otherwise, there's better options out there.
Basically, don't OPEN a tree unless you plan to use the rest of it (Exploration is an exception). Its not worth the culture hit otherwise.
On Emperor+ the AI cheats and the only way to win is to cheat back. Download mods that appeal to you and use them to your advantage. That's how the game is played online. Talk to the No Quitter (NQ) group if you want to learn more about the cheat mods that they use.
I think you need a bit more practice. Civ is a bit weird in that, strats that are the best at low to mid difficulties are completely worthless and have to be thrown out at higher difficulties. Usually in a game, its more about executing the same strategies more effectively, but Civ has always turned this on its head.
Namely, at higher difficulties you often have to give up on things like Wonders and even Religion, and instead focus on being extremely efficient with your tech, cities, and growth, and take advantage of the AI's inefficient play to get ahead by the endgame.