I'm well aware that bots to run your country are illegal and I'm not planning on using any either. (Where's the fun in that?)
I did come upon a little annoyance where I was buying on the market and reselling on private.
I had to refresh the 'control'page each time to see if there are any changes to my countries.

My question is: is it against the rules to use an autorefresh-website (like pagereboot.com)?
It doesn't do or change anything to the country or game, except from refreshing the page every xx seconds.

As long as you don't use it to wall while you are sleeping. I could be wrong.
I found that out the hard way.

The only thing the site does is refresh a given link every xx seconds.

And when I'm sleeping, I couldn't care less about playing a game. There used to be a time where it was otherwise, but I think I'm getting too old for that. :P

Should be fine as its not sending data to the game only refreshing the page.

contact server's mod aka littleitaly.

regardless of intention its not allowed,

"Automated scripts, bots and macros
Earth Empires does not allow players to use any form of script, program, macro or other software tool to perform user actions in an automated manner. Scripts that enhance game play by helping users complete actions quicker, such as auto-form fill fields, are permitted. However, these must not play the user's country without user input.
In addition, players are not permitted to collect news, scores, or market data with scripts or bots. For players who wish to use such data, the Earth Empires team grants API keys to developers. These keys can be obtained by contacting Earth Empires Staff directly via e-mail or through live chat. API codes are given out on a case-by-case basis: applying for a key does not automatically mean a user will be granted one."

pretty much anything where you are not physically involved is not allowed.