Can somebody explain discrete time frequency
Continuous frequency is the angle the waveform travels through per second. This is either measured in cycles per second, Hz, or radians per second.

Discrete time frequency is the angle the waveform travels through per sample time. Though it can be expressed in cycles per sample, it's usually given in radians.

In your case, a 100Hz signal sampled at 44kHz goes through 100/44k cycles per sample (about 2.3m cycles), or 2pi.100/44k = about 14.3m rad, usually given the symbol \$\omega\$.

The benefit of this method of expression is that you can write \$x(n) = \cos(\omega n)\$ where n is the sample number.

If you take M samples and do a DFT, then k is usually used to refer to the DFT bin number that corresponds to that frequency. \$k_{\omega} = \frac{M\omega}{2\pi}\$, obviously leave out the 2pi in that expression if using the cycles per sample form, instead of the radians per sample form. k is also the total number of cycles that occur in M samples.

In your case, with your record 10 seconds long at 44kHz, that's M = 440000 samples. k for your 100Hz sinuosoid is 100 cycles in 10 seconds = 1000. That is, in your 440k point DFT, the 100Hz signal will show up in bin index 1000 (1001st bin if we're indexing zero based). To check, 2.3mcycles * 440k = 1000 (to within rounding error).