There are five seats left in Business Class (NOT 5+4+2!). If my recollection about CORDA is correct, there are at least seven seats in Economy - I seem to recall that CORDA only counts to seven and that seven means "seven or more than seven" (I was trained on a different and now obsolete reservations system in the dim and distant past, which counted up to nine). The fact that it shows M7 S7 L7 etc does NOT mean that there are seven or more seats in each booking class, it means that there are seven or more seats in total which may be booked in any of the available classes. The fact that these seats can be booked in all classes, including the lowest ones, probably means that there are a lot more than seven seats available in total.

Different codes mean slight different things with different airlines, but
V and T are generally special fares. L is at the low end of the regular fares.

I can't answer the question about whether or not you would have been able to book your flight in a lower class. Generally this doesn't just depend on what is available on a specific flight, in many cases it also depends on what is available on other sectors of your itinerary as different fare classes can't always be combined. Also, there could be other restrictions - e.g., there may well be seats available in V but they come with a minimum or maximum stay requirement.

As for upgrades - I would agree with you that an op upgrade is unlikely.