Are silver dollars (Morgan/Peace) legal tender coins or just collectible items? Is a fake Morgan/Peace dollar counterfeit currency?
Yes, they are legal tender.
31 USC 5103: United States coins and currency (including Federal reserve notes and circulating notes of Federal reserve banks and national banks) are legal tender for all debts, public charges, taxes, and dues.
They are United States coins so they are legal tender. The age of the coins is irrelevant and I don't think that the US government has ever revoked the legal tender status of any of its coins or currency.
(Of course, their value as legal tender is still one dollar, so you'd probably be foolish to spend them that way.)
It is illegal to counterfeit them:
18 USC 485: Whoever falsely makes, forges, or counterfeits any coin or bar in resemblance or similitude of any coin of a denomination higher than 5 cents or any gold or silver bar coined or stamped at any mint or assay office of the United States, or in resemblance or similitude of any foreign gold or silver coin current in the United States or in actual use and circulation as money within the United States; or
Whoever passes, utters, publishes, sells, possesses, or brings into the United States any false, forged, or counterfeit coin or bar, knowing the same to be false, forged, or counterfeit, with intent to defraud any body politic or corporate, or any person, or attempts the commission of any offense described in this paragraph—
Shall be fined under this title or imprisoned not more than fifteen years, or both.
(In case you're wondering, the counterfeiting of nickels and pennies is covered under 18 USC 490: still a crime, but the penalty is less.)