Limited number on the racks/launchers but the total number carried for reloading could be almost anything.
http://pwencycl.kgbudge.com/D/e/Depth_Charge.htm
Specific sentence;
"The typical loadout on a fleet destroyer was about 30 depth charges, while dedicated escort ships had a very large loadout, of as many as 300 depth charges."
No data I can find on how long it took to drag the extras up from the magazines or prep them for firing/dropping. My problem with the whole thing is it's too easy in any depth over 300 feet, the thermal layer acts like a Klingon cloaking device. Fire all tubes, dive 60 feet below the layer, slow to 2 knots, go five miles in any direction except the original convoy/task force course before coming back to periscope depth. Don't even need to go to silent running, once I'm under the layer they can't find me at all. I tried adjusting that at one time but the layer seems to be completely digital, either 100% effective or zero percent.