F1 visa student, working online at home country as a publisher for US based company

[HERO]

Hey experts,

It is summer and I am interested in working. However, that is working online. So this is what the overview of my work would be like:

Note: I have an F1 visa

1. I run a website
2. I signup with a US based company
3. I publish their ads/offers/surveys and make money
4. The US based company requests that since I am a non-US resident, I fill out their W-8 Form and Compliance Certificate.

In the case I do fill the form and comply with their terms and make money, would it be breaching the visa terms I agreed to? Note that I would NOT be doing the work when I am back in the US (at least that is the plan).

However, while I am back in my home country, would it be a problem if I did do some internet marketing for this US based affiliate network?

Could it potentially harm my chances of obtaining the Green Card later on?

Thanks guys.

[EDIT]
Oops, could I have this post moved to F-1 and J-1 Student Visas forums? Thank you.