If I incorporate a company in Singapore, get an employment pass and assign myself as a company's director, do I need to really live in Singapore, or I can control my company from abroad?
After the May 2014 changes to the Entrepass scheme, what you propose is basically not possible anymore. The Entrepass is no longer suitable for solo entrepreneurs, and you cannot open a company without a resident director, who must be a Singapore citizen or PR.
The usual workaround is to hire a nominee director (~S$1500/year) and then get that company to apply for an EP for you. This is a moderately expensive and risky proposition, and the bar for getting an EP keeps getting raised higher and higher: you're currently looking at a likely minimum of S$8000/mo in salary, from which you have to pay Singapore taxes.
While I'm not aware of any official residency requirement, an EP is intended for someone who is working in Singapore, not an absentee director. You would at the very least need to find a residential address in Singapore to "stay" at least on paper, and at renewal time (usually 2 years) you would likely get some pretty pointed questions from the Ministry of Manpower.
On the other hand, if you choose the nominee director route, you can get effective control of a Singapore company without an EP or physical presence, which is likely what you wanted anyway?