Dollar coins are still accepted and are even given out as change. I went to a museum and they gave me back dollar coins as change.
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The word "still" isn't really applicable here. $1 coins are in regular production, with many millions being made every year. They're accepted by many vending machines, supermarket self-serve registers, and by transit systems. In parts of the country with highly automated transport systems (e.g. Washington DC) the coins are in common use because they're given as change.
The only problems are that poorly-trained clerks may not always recognize the coins, and there is a persistent but FALSE urban myth that the coins contain gold; in reality they're made of about a dime's worth of brass.
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Yes, absolutely. Unless they are counterfeit (but that is true of all Coins and Paper Money).