Could a submarine first a torpedo up a surface ship, or could surface ship with torpedo tubes fire a torpedo down at a submarine?

Acoustic torpedoes are designed to do exactly that.

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https://en.wikipedia.org/wiki/Acoustic_torpedo

Depth charges have ejector systems that lay down a pattern. The thing you have to realize about WW2 ASW was just keeping the U-Boats running deep, was preventing them from charging/hunting. Thus even unarmed aircraft flown by bush pilots, hobby pilots, and so on, were sent out to harass U-Boats because German SOP was to dive whenever they spotted an aircraft. Therefore, the practice of depthcharging the hell out of each and every ASDIC contact made sense even if most depth charges did not result in a kill. The convoys moved on while the destroyers and U-Boats played cat and mouse, that was the point. When they did get a kill, the Germans could maybe replace the boat, but they ran out of experienced crews. Obviously; a lot of destroyer crew survived the war, U-Boat crews not so much. 

https://www.youtube.com/watch?v=8nLPntkaiW0

If I blow something up, wouldn't there be pieces of such in that explosion. Something about understanding pressure in water. How does that work? What's the scientific principle allowing me to understand that yes. I like a big boom!?!

Understanding is... What are you trying to ask? How do things function underwater? Did those Mythbusters show something on this?

Umm.....you SHOULD know that subs have been firing torpedoes against surface ships for well over 100 years now. Modern technology since the 1950-70's (not sure when it started) have allowed surface ships to fire torpedoes against subs.

The original depth charges work just like you think. They are set to explode at a certain depth and are rolled into the water. They often did detonate near the sub. Shaking the Hell out of the sub and crew. Any military history program on TV or on computer will tell you that. The trick is detonating close enough to the sub to crack it like an egg.

The "Hedge Hog" was a big improvement to the depth charge. You have a computer. You can look that up yourself. In fact, you can find much more on-line with your computer than anyone can tell you about here. The same goes for most any topic.

Both are possible. This isn't even REMOTELY an either/or issue.

Depth charges are set to detonate as a predetermined depth below the surface. There was always an degree of guesswork what depth to set them for.

Torpedoes are fired Horizontal from both Submarines and Surface Ships,  Not Up or Down.  They then proceed through the Water towards the target and change depth as required.  They are guided by WIRE connected to a guidance computer on the ship and by active sonar built into the nose of the torpedo.   That is Today.

During World War Two,  Torpedoes were fired but did not have any controls after they were fired.   They either Hit the target and exploded or passed under and the Magnetic exploder set them off.

World War Two Depth Charges were either dropped over the Stern or launched some distance with a special device.  The Ship used sonar to locate the Submarine and when directly above the Sub, they dropped the Depth Charges. There is a setting on the Depth Charge to make it explode at a preset Depth.  

subs can fire porpeados from below the waves up at surface ships

surface ships or aircraft can launch torpedos at subs under the waves

depth charges were set to explode at a predetermined depth, the ship had no way of knowing what depth the sub was at, other than knowing the depths a sub at that time could decend to

It is much easier and far more likely that a sub will take out a surface target than a surface target taking out a sub. - which is why where there is a fleet, there are usually friendly attack subs lurking not far off helping to protect them along with various airborne anti submarine warfare assets.

Enter ASW Patrol aircraft....like the Orion, Poseiden, Aurora, Nimrod, Atlantique, Bear, Dolphin etc and various models of Helos (Sea Hawks, Sea Sprites, Helix etc) that can carry and drop torpedoes, mines, depth charges...etc

They can patrol the coast and/or in advance of a fleet to set up picket lines around them by dropping Sonar Bouys (and dipping arrays lowered from helos) to passively monitor and/or actively "ping" subs to get exact locations/depth to compute firing solutions.

Because of an aircraft's ability to locate and track passively, unless they come up to periscope depth for a look around, most subs won't even know that they are being monitored or followed from the sky until they hear the active "ping" followed by the splash of weapons entering the water.

The problem for surface ships is that submarines are designed to be as quiet as possible. It is easier for a submarine to detect a surface ship and launch a torpedo than for a surface ship to detect a submarine and fire a torpedo. This is why, in WWII, German u-boats were so effective at controlling the Atlantic.

Even today, submarines are tough to detect. US carrier groups head out with submarine escorts for exactly this reason ... the best way of detecting and killing an enemy sub is with your own sub.

Depth charges are high explosives with a trigger set to go off when the pressure reaches a certain value. When you roll them into the sea they drop, the pressure builds as they go deeper, and at the set pressure/depth BOOM!

The idea behind them was that you could drop several together that would detonate at different depths. The high explosive compresses the water around the depth charge to form a huge hydraulic pressure wave that could damage the hull of the submarine. By ensuring they detonated at different depths you'd try to minimize the chance that the submarine would be deeper or shallower than you'd set the charges.

In other words, depth charges didn't need to hit a submarine to damage it. It was the underwater 'blast wave' that could also do the damage.

In the olden days....... they had sub spotters........looking for the tell tale periscopes or it's wake.....if it was near enough the surface.  You also had plane spotters.

Another way  was when you spotted , or were HIT by a torpedo.......then you had a pretty good idea which direction the sub was.

Depth Charges worked by exploding  near the sub.  The concussion wave is amplified by the water...........making it extremely deadly,  even in close promixity.......you didn't need a direct hit. ....but of course,  with sonar, and more modern techology......you could  practically drop a charge right on top of the sub.

Yes, submarine fire a torpedo up at a surface ship. Something they've been doing that since 1914. Why couldn't they?

Yes, a surface ship with torpedo tubes fire a torpedo down at a submarine. Again, why couldn't they?

Rolling depth charges was the most common way. You'd locate the sub or where you think it is, sail over that spot, roll them off the back and hope you get it because you had to set at what depth the charges would detonate and hope that you got it right. You would know if you got the submarine if the explosion of water was stained with oil or debris. If you missed then you would have to wait several minutes for the water to calm down as the turbulence of the underwater explosion effectively blinds sonar. The British designed the Hedgehog system which fired several mortars with contact fuses. This was fantastic improvement. You can fire from range, have the mortars spread over an area to increase the hit chances and more importantly since they were contact fuze you know you hit it if there is any explosion at all. If there wasn't then you can fire again since your sonar wasn't blinded by the miss.