I have also struggled at Emperor. In the last game I played, Rome's capital spawned within 10 tiles of mine, and Rome promptly settled a city right between. I immediately began building military units when I saw how close they were. I was at war within a few turns and surrounded by 5 warriors. The ONLY REASON I didn't lose the game before turn 20 is that barbarians attacked Trajan from the back and he inexplicably didn't finish me off. My capital was beaten and ripe for the taking, he had 3 warriors with enough health to win, but a barbarian horseman hit him from behind, and he turned all of his warriors around to attack it, losing one in the process. I finished a warrior built that turn, killed another, and he probably STILL could have finished my cap with his last one, but he ran. I then went FULL ON SCORCHED EARTH MOTHER fudgER and raised a gigantic military and took him out. It was agonizingly slow, and I probably blew 50 turns screwing around with JUST getting back on my feet from that. When I finally finished Rome off, Scotland and India DOW me, I held them off, then 2 more. I spent the entire game fending off attackers, but after Rome it was actually pretty easy, I expanded where I could, got about 6-8 decent cities going, popped out another 3-4 late game. I was going science but I ended up winning culture before I even got a spaceport up. I hadn't even realized I was even in the running for it.
I also played an Emperor game as Korea that was similar except I was endlessly harassed by barbarians FOREVER. They actually took two cities at one point, I was down to my capital. France got one back, then I DOWed to get it back from them. But once I stabilized and could defend myself, I poured on the science and cruised to an easy, lazy victory.
It's those first 50-100 turns that are murder, and I feel like I'm not only behind but getting further and further behind. if I can't find room to establish about 6 good cities, I need to conquer them. And more often than not, I've got no choice but to conquer, there's rarely room for more than 2-3 cities beyond my capital.
I'm not yet winning consistently, I've had to restart my Wilhelminia game a few times. My early wars just ... don't go well. I don't really understand well enough how all the bonuses and stuff work, like flanking, support, etc. I need to read up. The game is hard enough at that level that you can't just screw around and win easily. or at least, I can't.