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i got a similar idea and i d like to open in the US, but it's quite hard to open a bank account for a non resident.
AFAIK There are specialised companies out there that offer offshore business registrations including a virtual office, registered local agents have you find out where to start?
The corporation will pay tax in that country based on corporation's income.
Although the browser application case, another feature is the fact that the user is uncomfortable page refresh event. If you want to only written with omegle video and voice conversation, you can too if you want.
Omegle Video chat section you will need java support to use.