shallow, clear, marine waters with vigorous current activity
Limestone.
conglomerate
clodudy
yes
Sedimentary.
Limestone.
It's always in a sedimentary rock, but mostly they will be found in a limestone. Some limestones, like the 'shelly' limestone, will be more likely to contain shells than others, like the oolitic limestone (which is not made out of shells). Again, bones will tend to be found in sedimentary rocks, but the actual bones will tend to have dissolved and been replaced by rock minerals which precipitated out of solution to fill the 'mould' left by the bone (unless they were deposited recently, in which case you're more likely to find them in unconsolidated sediment like sand/mud).
a location where the crust has been downwarped by tectonic plate motion
Limestone
limestone
Calcite
The metamorphosed limestone will most likely be a skarn or marble, both formed from contact with an intruding granitic magma.
conglomerate
clodudy
yes
Sedimentary.
Coal.