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Would companies know that you only have 2 years available on the H1? Just a thought, but they may not want to sponsor someone if they only can stay for a couple years. Might make sense to think about applying to a few European schools because then you could come back for the full 6 years.
i have had to do some work with visas. My best advice is to contact a consulate and ask them the questions. they tend to be fairly responsive. Another tactic is to contact a consulate of a small country where they are not bombarded by e-mail...
Seriously all your immigration questions can be answered better on immigration portal. There are some gurus there
ToDoOrnot, assuming you are going to school in 2008, you would would have completed 4 years on your H1. You will still have two more years left. Additionally, if you did not do your Master's in the US (and already use your OPT) you will get an additional year on OPT(Optional Practical Training).
Keep in mind that if the economy is decent in the US when you graduate, most employers will be willing to sponsor your green card along with your H1. If your green card is getting sponsored by your company, you can keep renewing the H1 visa past the 6 year limit - unless you lose your job in which case you will need to find another company willing to sponsor your immigration.
So, short answer, yes, you will be eligible to work in the US, under certain conditions.