Rust is a general problem, but “stainless” doesn’t exist. Stainless steel is made by using an acid on the outside layer of the metal. Then only the outside atoms are ionised and can’t oxide/corrode. Once you submit a stainless piece of steel to acids or cause a slight crack/damage/streak in the outside layer of the stainless steel, it becomes useless and it corrodes much faster on the inside than normal steel.
As mentioned by Daniel, in the marine environment it is rough, the salinity and temperature differences constantly attack the skin of the steel construction, if this would be stainless steel, it would get damaged equally fast and cost much more.
Another point Daniel mentioned is also right, if you want to weld such, it is very hard not to damage that outside layer and your welds themselves will corrode causing a severe danger for cracking.

As for strength, there are compounds that are much much much stronger than steel, yet the creation of steel makes it cheap as there is plenty of that around and it’s easy to manufacture. If you look at those compounds you get a totally different story. For now the only intended application for such compounds is in some of the submarine sonar domes. Also in Compressed Natural Gas carriers. If they wanted to use steel in such carriers, it would require a hold wall of 1m concrete steel to reach their required safety level. Needless to say they would have little cargo and a hugh empty weight. Therefore they want to use compounds for that application. But even then the safety requirements are too high and the idea is just rising with a few (4 or 5) designs on the drawing boards.
I expect that this will become reality in the near future as Natural Gas has become increasingly important. Once those compounds are used, I think they will start using them in warship construction too. Submarines would then be easily capable of diving much deeper, although it should also be mentioned that some compounds have some serious weaknesses too. Shafing resistance, acids, chemicals, temperature differences are some of them depending on which compound is used.

As for structural strength, they are calculated for a hull life. The hull is of sufficient thickness to withstand all those years of constant corrosion. They X-ray a hull to know the thickness every once in a while.
One of the drawbacks of the strenger steel versions, like HY-80 and other high tensile strength sorts of steel, is that you can achieve the same strength with less material. For example a hull of 5cm thick HT Steel can be equally strong as 10cm thick “normal steel”. This is good as the weight of the HT Steel will be much lower, so there is more stuff to add. BUT, here is the tricky thing, they’ll last much less long. Corrosion on both sorts of steel goes equally fast, this means that after one year, the HT Steel example only has 4cm left while the other one still has 9cm left. This means that the first, strong, hull would have lost 20% of its thickness and of course a proportional equal part of strength compared to only 10% for the second, weaker hull. Hence the downgrading of the stronger steel versions is higher.
The “grating” you often see in ships is also caused by this thinner hull. The wind dents these hulls so you can see the construction frames inside. They actually dent and tear easier than regular steel too. But, as said, it saves a LOT of weight.

Shadow, there already was a plan for new Su-33, at first there would be an upgraded version with better electronics matching the Su-30MKK, the version after that would be equiped with Yakhont/Moskit and other anti-ship missiles. Not sure if they will go through with that, if the carriers are indeed to become smaller, than this aircraft would simply be too large (which is already a problem now).

There is no such thing as a “second Amur”, in fact, there is no such thing as an Amur at all, for the moment. Kronstadt was only laid down in July, the third one a few weeks ago. There was no Amur building at any moment. The “Kobra” picture that surfaced was just Sankt-Petersburg herself under construction.

Glonass is by no means reliable. It’s degraded and the system is just very very very faulty as they didn’t release their world system yet.

The one you show is a Priz type DSRV, they really don’t go that deep.
Mir is probably 1837K.

Haha, that’s the “at anchor/moored” flag. It isn’t necessarily the national flag, but often it’s done so, although not officially a national flag as the dimentions aren’t “official”.

As for “hydrodynamically advanced”, that’s a wrong impression. The highest speed shape underwater is a “cigar”,every transverse cross section has to be a circle, then you have the fasted shape below the waves. That is also the idea behind a torpedo.

As for the “teardrop”, it gives better stability and has advantages over a “cone shape” because the broader part in front creates a certain turbulation that makes the rest of the body have less drag/turbulences. So it’s better than a cone/missile shape, but it’s slightly worse than a “cigar” (revolution body).

Both pictures of Tigr, both courtesy of Ilya Kurganov.

Pantera:

As already mentioned “better” is not the word. It offers better steering, but also has the disadvantage of slowing down as all four of the blades have to be used to keep her on her heading. A hard thing to do and for nuclear subs it would make more noise and slow them down. For small subs no problem, short distances, less environmental problems. For larger diesel subs, their operational theatre is again a bit rougher than the Baltic and often currents have worse effects, add to it the already hard course-keeping of the sub.
But, due to the four rudders, the sub is capable of turning around much faster than a normal sub, and as an extra advantage it offers better bottoming capability, which is for a nuclear sub not a likely thing to do anyway.
Steering has always been a pain in the *ss for submarines as their propellor is behind the rudders and not in front of it as with surface ships. In fact the LA or Ohio class were the first submarines in the world to be capable of turning (altering course 180°)within 4 times their own length. Not sure which one of the two it was.
This is possible with normal rudders, but an for an SSK a much shorter turning circle and manoeuvrebility come in handy.

And as mentioned before the forces of a heavier submarine on the X-tail are rather annoying too.