Man phenomenal.Engineering. Metal. I used to be obsessed with submarines. Russians have some nice ones, Akulla class... the g Americans and their Seawolf. Of course the iconic German u-botats there's one in a smithsonian museum in Chicago I think, it's nuts. Those 12' long torpedos or longer with contra-rotating propellers... nuts.
Machine shops aren't uncommon on naval ships. Such a well supplied one is perhaps unlikely aboard a submarine, but missile subs are the largest and generally the longest-cruising of any type, so it makes a deal of sense they'd have as much capability for self-maintenance as possible, especially given their vital deterrent role. Same goes for the pool et cetera - the human crew being as important to the mission as the boat herself, and just as much meriting maintenance.
There was a National Geographic documentary[1] about scrapping one of the Typhoons. I could only find a Russian language version on Youtube[2], which it's still fun to at least scan thru quickly just to see the scale of the thing
According to https://en.m.wikipedia.org/wiki/Typhoon-class_submarine of the 6 built, 3 are scrapped, 2 retired, and 1 in service (though later on that same page it says the last SLBM of the type used was decommissioned in 2012).
Based on the pictures, it definitely doesn't look like in service. Also, seems quite strange if they'd let civilians (?) run around and take pictures of a strategic weapon system in active use..
Not without sinking. The ballast and trim tanks won't suffice to give that much up-angle; you'd need to flood some after compartments to make it happen, and that is a very bad idea, especially since you would not also be able to maintain neutral buoyancy.
Besides, why would you want to? Your missile tubes are configured for vertical launch anyway, and it's not as though you can just pop a missile out, haul it through the corridors to the forward torpedo room, stuff it in a tube there, and fire it. Every one of those things isn't a thing you can do.