Great questions
The golden factor for countering submarines is screening efficiency. If you spot a submarine engagement, check to see the screening efficiency covering the convoys (if any), torpedo to-hit chance is directly correlated. 100% efficiency, 0% hit chance. 50% efficiency, 50% hit chance. Every point of torpedo attack (the stat) is 1 shot. Screening Efficiency is also true for Naval Battles in general, if you have torpedo-equipped ships, they will *only* be effective if your enemy's Screening Efficiency is low, either because of bad task force composition (they have too few destroyers), you have ships dedicated to killing enemy screens (generally Light or Heavy Cruisers armed with light weapons), or they've doom stacked and have fleets which are far too large (inflicting a pretty hefty Screen Efficiency penalty).
This means if there is 100% screening efficiency, then no matter how many submarines there are you will *
not* sink *
any* convoys. Hence I also had Naval Bombers to hit enemy screens, to reduce screening efficiency.
The second factor is escort efficiency - that's the speed at which destroyers will respond to a call for help from a convoy. Fleet in Being has excellent escort efficiency while Trade Interdiction is terrible (hence at the start of the MP game, I confirmed that Bo was going to build destroyers, as that told me I could focus on my subs and take Trade Interdiction). I know Convoy Raiding Efficiency also plays a part, but I think that's more to do with having enough Submarines to properly cover the zone / convoys passing through rather than spotting. Not entirely sure on this.
Now, regarding Cruiser Subs it gets a lot more complicated. Submarines do still need to spot a convoy to intercept. Surface Spotting (Surface ships and Subs have this), Naval Intel and Naval Intel Efficiency (on a per-Naval region basis and done by air recon generally) all factor. Regular submarines are not great at spotting, hence I made a big deal about getting Scout Planes up in the air as soon as possible. Heavy Fighters and Tactical Bombers are also acceptable at this task. For areas outside of air coverage you'll want either Surface spotters (Cruisers with radar / float planes) or Cruiser Submarines armed with Float Planes (the only sub class that can use them).
Regarding quantity, Cruiser Subs are significantly more expensive and also easier to spot by enemy escorts so you do need to be careful with them. You could do a separate Task Force with cruiser subs set to Do Not Engage, though I think that would only spot a single naval region, or you can add one to a regular raiding task force, but then I'd make sure they use Snorkels. One thing I forgot when doing my test run is you can manually set classes for different ships (the turret, shield, skull, etc icons in the ship designer). Set a different icon for the Cruiser Subs Vs the Regular Subs and you can control how many are automatically added to a Task Force.
One thing I should add regarding Greece in particular, and their Cruiser Submarines. Greece has the Mediterranean Design Company which decreases range by -50% and cost by -25%. What I did was apply the designer *after* I got the focus which gave me cruisers. This way I had super-long range, expensive cruiser submarines to attack any tough to reach areas while my Sub 3's were researched *after* the designer so they had poor range but were cheap and could be mass produced. Thankfully we didn't come up against heavy naval bombing else the range could have been more of a problem, and when we did start to face some, I added snorkels to counter.
Once at war, I don't generally refit submarines as I find its more important to just get more ships out, especially if you're trying to cover large areas or multiple theatres as I was with Greece. The only exception would be if I was losing a lot of vessels to good enemy escorts then I'd refit with Snorkels. Radar's not normally worth it unless you have excess capacity or are lacking manpower.
Edit- Oh, last thing! Engagement Risk matters a lot for submarines, far more than for any other task force type. Low means they will target only convoys and will run if they see destroyers. Medium means they will engage vulnerable capital ships and convoys, and High means they will even try to hit destroyers.
