🚀 go-pugleaf

I have read a little, experimented a little with the FFT. And I have 
a question.

This about sums my experience: I have a simple program I converted from 
BASIC to C which asks for the frequency, amplitude, and phase of four 
sine components, and then calculates them and sums them into an array. 
It then deos an FFT on them, analyzing at n/2 intervals where n is the 
number of samples. 
 
Now: if you enter sine values that "hit", which is to say are identical 
to those at which the program analyzes, the output is clean: a well defined 
line where it should be. But if the sine is just a little bit "off", the 
results are of course dissapointing and difficult to interpret. 
 
Can I "zoom in" on that frequency range, for better resolution, without 
increasing the sample rate or making any other changes which in the real 
world (if I applied this to CD audio for example) would be difficult? 
Don't ask me why I haven't tried by modifying my program...
 
If I feed the output of this program into a reverse-FFT algorithm, will 
the original waveform be faithfully reproduced? I would think so.
 
Should I perhaps be looking into the Fourier Transform proper? I hear it is 
a nightmare but is "continous", whatever that means...has a nice ring.

Thanks for any input. If you don't feel like typing out an involved 
response send me your phone no. via e-mail and I'll call you.