If you play on (example)US1 and US2, you have access to your gold on both worlds. If you restart on US2, you will lose your city and everything built in that city. You will also lose any advisors or inventory slots that have been paid for. I would suspect that includes all the inventory.
I'm not sure about what you mean in that part. Do you mean - you are playing on US1 and start from scratch on US2. Or - you are playing on both US1 and US2 and you restart on US2.
If it is the first case, then this is true.
If it is the second case, then it is wrong. If you restart, you will keep the advisors for as long as they are paid for. I'm not sure you keep the inventory slots and what they contain, I know you keep them when you are rimmed, but I don't know what happens when you willingly restart.
Does that include any heros that you might have? (if it is that type of world)
The heroes stay with you when you restart a world. However, they do not come with from world to world (like the advisors).
Also, how would I restart near alliance mates from (ex.)US1 that have come to (ex.)US2 if we are not in the same alliance on US2?
If you are not on the world yet, they would have to send you an invite, with the button shown in the image below:
As it is said below the button, you will directly join the alliance and will start near the alliance members. The button will generate a link, they'll just have to send it to you.
If you are already on the world and want to restart near them, you must join their alliance, then use the restart button (in your settings), the game will send you a link via e-mail, and once you click on it, it will give you a choice between choosing your own direction or join near alliance mates.
If you have any other questions or something in my post is unclear, feel free to ask, I'm a bit tired and may not be clear