No, the problem is not playstyle. I've tried maybe 10 starts (deity, standard speed, continents, no ruins, no barbs, quick combat). No wonders built, not settled close to the AI (if 2nd city settled at all, usually away from AI but you have to settle SOMEWHERE).
Well diety is widely regardly as a different beast entirely given the AI unit advantages. In every Civ game, it is considered different and is meant to challenge the human players and allowable exploits are expected to be used to counter those massive advantages. Fastest way to get your 2nd city/1st settler out in any game is to beeline for liberty path. That's what I do when I have a crowded start. I beeline for that 1st settler and the 50% build bonus. Then you can dump your gold and get a 2nd settler right away if you need to.
I've started next to Wu, Ramesses, Monty, Elizabeth, Alexander, Oda, Darius, Ramkhamhaeng and Isabella. They have all declared on me so leader doesn't seem to matter, one time (next to Alex) he didn't declare before turn 53, but else I have consistently been declared upon between turn 13 and turn 50.
Without knowing your game, it's hard to discuss, but WuZetian, Monty, Alexander, Oda all have agression of 6 or higher. You're just extremely unlucky here and it goes back to my comment that Civ5 starts can vary in (actual) difficulty wildly on the same difficulty setting and 'canned' starts don;t work as well in this game as in previous games, though canned starts is probably ok to stick to in prince and below. But given so many warmongers were around, I am surprised they didn't war each other as well, giving you room to expand and play lackey to their coalitions. Unless you massively misplayed your hand, or did something wrong or again, just unlucky that they are arranged in such a way that they all had to attack you first.
Also, there's the dogpile effect. If you're at war, there's a very obvious penalty applied to AI's view of your military strength and even weaker or civs on par may declare to try to gain advantage. This of course can also be used to your advantage given the AI isn't great in tactical troop movements and you can tie up easily, 1 or 2 AI's forcing them to waste their production making troops you kill while you keep your heavily promoted units.
I don't mind the AI doing an early rush in some cases, but seriously? I've even tried going straight warriors and archers while still having a decent distance to AI, even that didn't prevent war. Most games I tried only monument before military (getting worker and settler from liberty), but the AI just consistently declares war.
Again, without seeing your game it's impossible to discuss. That said, I am confirming the AI will DoW early as part of their slate of possible strategies.
This is not a problem, and defending against this eventuality is part of high level play.
To me this is not only extremely predictable, it's not fun and it's just a cheap way of making the game harder. And of course, it doesn't matter if the AI is friendly when you meet them or not. They'll declare anyway.
I can't say for sure, but you are probably playing a difficulty setting that perhaps is beyond you or you're sticking to a starting strategy that isn't suited for that partiuclar start, but worked well in another game and you didn't adjust. That's fine, I fail a lot of my starts, but that's fun. Maybe you had a good start on diety once and think you're diety level, but as noted, ACTUAL difficulty of Civ5 games can swing from game to game.
There are some games I've played that I feel should be rated much lower because of the AI selection I drew, their placement and early wars, and how they cancelled each other out, allowing me to easily breeze through the game.