a)Can a sub detect an aircraft? Yes it can, and not only due to satelite -or any other kind of- datalink. Subs have one radar to detect both naval and air targets. However, using it is a huge risk and the reason is obvious: the sub's position is revealed, the ASW airplanes and helos gather around and the poor sub ends up playing chess with the "Titanic". The safest way for the sub to detect an aircraft is through ESM (Electronic Support Measures). ESM (known as Passive radar in the past I think) gathers mainly radar and -possibly- radio emissions via an antenna that comes out of the water (like the periscope), analyses them and comes up with the type of the emissive boat or aircraft. Given the fact, of course, that they do not use EMCON tactics (radar & radio silence).

b)How an aircraft can detect an enemy sub? First with its ESM sensors if the sub is using its radar, as I said above. But something like this is unlike to happen (I very rarely use radar in the simulator myself). So, the aircraft uses its own radar (A-G mode) and it has some very good chances of getting the sub, provided that it is on the surface. Otherwise the only way to be detected is with a dipping sonar (helicopter) or sonar buoys (aircraft). ASW aircrafts have another device called MAD (Magnetic Anomally Detector)used for ASW, but I'm not sure how that gadget works.

I think 40 US subs vs 120 USSR subs. Even US were better are outnumbered, so. .
But I think USSR didn't made so much subs to be only steel.
Oscar for ex. support a direct hit from one torpile. In august 2000 exploded 2 torpiles, so Kursk was destroyed.
Oscar is 3 times bigger than any US sub. Think about Typhoon more bigger!
Soviet thought very carrefully at the design, when decided to make such a sub - 30.000 tones.
For present think about Bulava!

USA didn't know so much about soviet arsenal, and thought they are weaker. After 1991 data begin to be revealed and USA saw Soviet was not so weaker.

The whole thing will not be very different from firing i.e a SUB-HARPOON. Initial targeting can be achieved through ESM. It is said that once out of the water, the missle will be able to be guided through the sub's combat system, but I doubt whether this will be usefull, since it will more likely require the use of radar. And of course, there is always the possibility that the missile will miss and the lucky pilot will pass the word to additional ASW assets.

Subs can pick up aircraft with their own radars though it gives away their position. Subs can also pick up some aircraft on their sonar if they fly near enough. US submarines would evade Tu-95's because the enormous sound of their engines made them audible even deep under water. Against other aircraft though this is not necessarily reliable.

Aircraft can pick up subs in a variety of ways. Sono-Buoys are common especially when trying to hunt submarines. The US relies more on helicopters than fixed wing aircraft for this, using helicopters to carry torpedoes to drop on top of sonar contacts.