There are a lot of assumptions required to have that statement be sensical including a lack of transaction fees (including, just, effort - you're assuming the time it takes for you to arrange the purchase and resale is without value) and extreme price stability. 100$ worth of peanuts isn't worthless to someone with a peanut allergy but it is certainly worth less than it is to someone without since to the person with an allergy the only value of peanuts is as a bartering currency.

not really. If you are planning an arbitrage operation, then their resell price (and thus value to you) must be at least MORE than $100, otherwise you wouldn't buying them and going through the hassle and opportunity loss of the arbitrage.

If you don't bother buying them, then the total value to you is probably less than the value of $100 for you.

It's possible that the value just happens to be equal to the value of $100. That's a vanishingly unlikely coincidence.

True. Value to an economist is an aggregate of all the individual’s values. Your individual value is likely to have not influence on the market value (unless you’re buying a lot at a different price).