My non-falsetto vocal range is about E3-A5 (those are the absolute limits, but really I only feel comfortable singing from about F#3-E5) [I'm an adult male]. I'm not very good at singing in falsetto and my falsetto range only extends up to about B5, which isn't really that much further than I can already sing. Also my falsetto is very weak and, above A5, almost squeaky sounding; I can't nearly achieve the fullness of sound that a countertenor can. How can I improve it?
Also, as a related question, how can I extend my lower vocal range? Comparatively, I have a pretty low speaking voice (I think it's around F3, although it's hard to say).
Alternatively, I suspect that I may be completely misidentifying my range and it's actually E2-A4. I sang in a college choir and I was identified as a tenor though so I don't think that's the case.