Yes, they're still being minted. Business strikes are produced in Philadelphia and Denver, with proofs for collectors minted in San Francisco.
There is no such thing as a Liberty dollar coin minted in 2000. There is however the Sacajawea dollar which was minted in brass, and unless in proof condition it is only worth $1.
The Sacagawea Dollar was minted by the US Treasury from 2000 through 2008. What year of mintage did you have in mind?
The George Washington "golden dollar" (actually made of brass, as was the Sacajawea coin) was minted as the first coin in the Presidential dollar series mandated in 2005. The Washington coin was issued in 2007 and the coins featuring subsequent US Presidents will be issued through 2016. Every President will have a coin, provided they have been deceased for 2 years on the scheduled date of issue. As of 2012, the coins are being produced only for collectors, and not for circulation, due to a huge surplus of the coins (which includes some Sacajawea dollar coins).
The One Dollar coins from 2000 to date. And starting in 2007 the US Mint has gave us One Dollar coins with MORE DEAD presidents on them, unfortunately these will last until 2016.
No US 1 Dollars coins were minted in 1907.
No US dollar coins were minted in 1983.
There is a mistake in your question. The Sacajawea dollars were not minted until 2000, so there would be no 1979 Sacajawea dollar. However, if you meant a 1979 dollar coin, those are Eisenhower dollars and are typically worth face value unless they are in exceptional condition.
There were no dollar coins minted that year.
There's more information at the Related Question.Two-dollar bills were never MINTED. Only coins are minted. Bills are printed.
Philadelphia
Yes, there used to be a gold dollar. There were three designs minted between 1849 and 1889. It was one of the smallest coins the US ever minted.
No US dollar coins were issued in 1809.