How to check that you aren't a brain in a vat: inflict some minor brain damage on yourself. If it influences your mind's workings as predicted by neurology, now you know your brain is physically here, not in a vat somewhere.
No, there's no way of knowing that you're not being tricked. If your perception changes and your perception of your brain changes, that just means that the vat is tricking the brain to perceive that.
The "brain in the vat" idea takes its power from the fact that the vat controller (or the vat itself) can cause you to perceive anything it wants.
If you are a brain in a vat then that should alter sensory perception. It shouldn't alter cognitive processes (say ability to add numbers, or to spell or the like). You could posit a brain in the vat where the controllers also have lots of actual drugs or electromagnetic stimulants read to go to duplicate those effects on the brain, but the point is that we have data about how the external world relates to us that isn't purely sensory.
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