Thanks a lot. Let me give step-by-step answers, ok?
The way you describe it, it sounds more like the challenge is that you're expected to qualify OOD very quickly...you say "weeks" where we'd probably say "months" at the very least. What is the reason for that?
Usually two to three months here, depending on the officers roster and availability of the escape ways. Say, in the same Comm Dept there are the officers who are under security protection from stand OOD watch as they have special watches within the crypto-protected rooms. Again, no engineers are eligible to stand OOD, it's a law - if your designator is marine engineering (either turbines, diesels, electricity, nuclear, DCFP special and so on, i.e. if you are in the guts of the ship), you are sort of Restricted Line in USN parlance. No bridge watches for them except for the EOOW on some ships where the main machinery dashboard is located on the bridge (up to frigate, but mostly corvettes). Again, the Dept Head always can screen some of his Divs from OOD watch if they have to deal with unreliable equipment. Say, on the Kirov-class CGNs the main AAW missile complex, S-300F "Fort" is served by two Divs and an engineer. The fire control system of that "Fort" is so whimsical that have those Divs let alone Eng standing the OOD watches they quite can be on hours off when the radar suddenly goes out of commission. All in all, not so many officers aboard even on a big ship are available to stand OOD, so one of the XO's main aims is to list the officers and held them to this watch.
For us, you start out as a Conning Officer, and at the very beginning you're probably getting a lot of direction from the OOD. Gradually you should earn enough trust that you can start making some decisions on your own.
Then as a JOOD, you should be an OOD U/I...basically an "acting" OOD to get practice doing what the OOD does, without taking on the responsibility for it all just yet.
On a cruisers we have the Deputy OOD which is uniting your Conning Officer and JOOD down and connected to the same reason - to introduce of the JO to making decisions on his own, but overall responsibility is on the scheduled OOD. In some cases they intended to hang the DOOD on some endless secondary inspections just to be free to do their job. There is neither habit nor the regulation about the mentorship in Russian Navy. On a smaller ships from DD down to corvette there is only one OOD, no deputy, no Conn, no JOOD. Sometimes the ship's NAV, if seasoned one, can enormously help the fresh OOD and usually does, but it is rather a tradition than regulation.
I've also seen it take over an year for folks who show up when their ship is in a long yard period. That said, it seems you provide pretty extensive training in your NavColl's.
It is rather the "surviving under pressure" experience. If you fail to pass the CO/XO OOD exam twice, you're nailed to be off this ship the next year and your career chances are reduced to significant degree. Not a problem at all - you can go to another ship and try again or got yourself ashore and spend your "up to 20" there, but with sufficiently lower salary and you will never be the ship's XO/CO, period.
Who teaches the new OODs? Does the lack of NCO's hamper the ability to train new OODs? Is that one of the reasons you found it so challenging?
Main teachers are formally XO and your Dept Head. But eventually it is up to you since everyone of them has a huge amount of more important (for their evaluation reports) jobs. Absolutely no help from the NCO. Some experienced Chief can only hold your Divisional job for awhile, allowing you to pay more attention to OOD deal, but he cannot help in the OOD preparations as such. There are no NCOs on the Russian ships' bridge - only a few of enlisted conscripts: a helmsman, a couple of lookouts, maybe an draftsman of the CIC on duty, all the others are commissioned officers.
What is the reason Russian OODs are expected to pick up marine engineering and weapons engineering?
Marine engineering - there are several occasions in which the OOD should personally direct the changes in the electrical commutations or machinery gears' setting. On some frigates the pitch of the propellers cannot be changed from the full spead ahead to the stop instantly, as it can damage the pitching gear on the shaft. If the remotely controlled switcher works properly, it is the EOOW's job but if not, the OOD by himself should know what he has to order to the conscript in the tiller/yoke room, where the manual drive of the pitching gear is installed, in step-by-step mode, as the EOOW sitting in his engineering spaces in the guts of the ship quite can has no real picture with understanding of the reason why the ship has to be stopped so quickly.
Weapon engineering is important to the OOD watch as there are constant troubles with loading/reloading of the big Soviet-type missile launchers at sea, which is extremely hard work. You should control along with the gunnery Dept Head the alternations of the connecting/disconnecting of the cables from the missile body, as any violation of that sequence can bring about a disaster with the missile's fuel fire and warhead explosion. Again, it is shared responsibility that makes the XO sure the things are doing in proper way. My own experience as just relieved OOD, as I saw it from the wing of the bridge, smoking - on Russian warships usually the forecastle's gun is installed, roughly similar to common NATO 76-mm OTO Melara, automatical gun named AK-176. While the turret/gunhouse of that set is manned, the main mode of usage is remote control from the gunnery officer command post, where the gun is controlled by fire radar, usually one named MR-123. Once on anchor, the boatswain guys were working of the forecastle while the gunnery sailors maintained the gun, turned to the starboard beam. Fire control radar was switched OFF but there were two naval cadets on a summer practice aboard, from some NavColl, who were studying the radar as they were ordered to by XO and their college's case officer. Ad hoc, they asked the bridge for a permission to switch the MR-123 emitting high voltage on, just to have two or three antenna rotation circle to fit the target position indicator in a proper illumination mode, and then-current OOD gave that at once, and I've just nearly swallowed my cigarette but that had been done. The circuits of the AK-176 are routinely configured in the way that logic prescribes: at the moment when the high emitting of fire control radar is ON, the gun automatically turns to zero bearing and zero elevation, to be able to react to the new target from the most proper position. That was what happened - gun turned and the barrel had hit one of the guys throwing him overboard. Happily we were anchored and the seas were warm and calm. A cadets were right, too - they should ask the permission from OOD as was ordered, but that OOD was not of gunnery or radar designator, he was navigator, and his carelessness quite could turn him to accidental killer...
You also don't seem to think on CO's/XO's too fondly. What is the reason for that?
Due to the fact that CO/XO are specialists forced to be generalists, too, pretending to be organic enough. They usually former navigators or weapon engineers, it is extremely seldom event to find a CO/XO from any other subcommunity. They either are struggling with their inherent designator's demons, simultaneously trying to show their leadership integrity for everyone. Of course there are good COs and XOs, but mostly they are very nervous and inconsistent in Russian Navy.
Is the foreign language requirement English?
Yes English especially on, say, Baltic sea with its extremely tough fishers and yachting traffic. I cannot speak Finnish, Estonian, Latvian, Swedish, German, Danish language, thus even plain navigation under COLREGS-72 there claims the English oral practice from OOD on a daily basis.