EI is paid to those who are available and looking for work, domestic or elsewhere. It does not matter if you are in Canada, the US, the Middle East or Mars.
First off, if you are on EI and leave Canada, that needs to be reported, especially if the reason is to work. Service Canada co-ordinates with CBSA regularly.
Second, if you work, that needs to reported, and the income as well. Again, it doesn't matter where this income was obtained.
You should not be offering blatantly incorrect advice like this. EI exists as a supplement to aid those that require a hand while looking for work. It is NOT a double-dipping resource.
Yes. This does not impact an EI claim as earnings.
However, it would be a massive ethical disgrace if an individual would elect to remain on EI even after winning the 6/49.