Let's say I create an online gambling site, where 2 players deposit money in an escrow account and they play. The winner keeps all the money, and the site keeps nothing (no fee for playing). Is this situation legal for the owner of the site?
Gambling or the provision of a place and means to do so, requires a license in most of the jurisdictions that allow it, even if no income and profit is made or is possible.
Gambling or the provision of a place and means to do so, without a license, is illegal in those jurisdictions.
Acting to support a crime or offence, either by action or omission, is called conspiracy, and this is itself illegal in many jurisdictions.
In most places in the world, no.
Running a gambling house (for profit or not) usually requires a licence.