Thoughts to the best of our knowledge are signals - electrical and chemical. So ultimately, thought have a physical form and aren't anything "ethereal".
Second question is unanswerable because with the premise that any answer/informatio you are given could also be a part of this "fake reality". It's an interesting question to debate, but it's not one that can ever be answered.
When you die, the aforementioned chemical and electrical signals seize. We might be able to "resume" this through resuccitation, though, but ifthat isn't done soon enough, your thoughts and your state of existence will be irreparably damaged.
These might be boring answers, but some philosophical questions simply have answers. What really messes me up is continuity of consciousness.
