2) It is impossible for a submarine of this sort to set a depth record for a conventional submarine - because the record would require a wholly different configuration. It COULD set a record for a military type (vice research type) conventional submarine. I would not want to ride on it when it did!
I think it was meant to mean a record for a PLAN submarine.
As for the numbers of Songs I would say at least 12 in service, because there are three flotillas of Songs, one for the North, East and South Seas Fleets. Each flotilla consist of 4 submarines. Note the end numbers for the Kilos are the same too. Houbeis are also grouped into sets of fours.
The pennant ranges however, show a greater number since they span from 313 to 329. That to me suggests 16 subs, and it seems to me that one fleet, the ESF may have two flotillas.
Although the Song is a successful design for the PLAN, the Yuan seems like a convenient evolutionary step to make since it apparently reuses many of the technologies developed for the Song. The Song's demise may have already been planned when the Yuan was arranged. At first the Yuan had to sort things, and in fact the great majority of the Songs were built after the first Yuan set sail. And now they got the Yuan fixed, and so shift the focus to the new hull. I think it was the Yuan the PLAN wanted in the first place, and the Song eventually became transitionary.
Still I really wonder how many Yuans the PLAN planned on building. If you have a successful nuclear sub program, there is going to be budgetary and doctrinal pressure against the diesel subs.