I'm not sure what the rod might have been, the inside of an air tank is pretty simple.
Replacement drain valves are available in a variety of configurations, and generally they thread into a nut welded into the tank. It's then just a matter of finding an appropriate replacement valve (relatively easy) and removing the old one (probably much harder).
To help get the frozen valve out, you could (should) try penetrating oil to free what are almost certainly frozen threads, but you may need to step up to using a torch to apply heat to help break the part loose.
You are correct that it is a good idea to use teflon tape on the threaded fittings, however no sealant is required or advised on the quick-connect part itself. These are designed to seal using internal o-rings.
There are multiple types of quick-connect air line fittings that at first glance appear similar, but are not necessarily compatible. It is very likely that you have connected two incompatible types, resulting in a leak. This is very common.
The two "main" types are often referred to as "automotive" and "industrial", though each can have sub-types that are typically letter designations, e.g. Industrial can be M, H or G. There's also a type called ARO, and one called Lincoln, but these are somewhat less common (at least in the US consumer market).
(image from Legacy Manufacturing)
The documentation for your air compressor may specify exactly which type of fitting you have. Otherwise head to the local big box store with your male coupling that leaks, and look for a similar-while-slightly-different male coupler to try.
Legacy manufacturing has published a very informative guide on the evolution of the various types of quick-connect fittings that lists the common types in use, with some images of each.
Milton Industries has also published a document that may help identify the type of plug you have, though their letter designations may not exactly match those of other manufacturers.
Best Answer
Some female quick disconnects latch the ring back as you describe. I don't expect you have an issue with the female quick disconnect on the compressor.
I suspect that while your male fitting appears to be the right "size", it is of an incompatible type. There are many different types that appear the same when held at arms length. See this answer for a primer on the various types of quick-connects.