I started working with HF frequency. Right now, I am working with 7 MHz frequency. I have been provided a range of 7-7.5 MHz. I have to divide that range into 132 distinct frequencies to assign each frequency to a different node. Please let me know what is the minimum frequency resolution for 2 frequencies which do not interfere with each other. For example, 7.001 and 7.002 MHz freq will interfere with each other or not??
Very basic wave propagation theory says:
No two different frequencies ever interfere in a linear system. So, any separation, no matter how small, of the occupied bands is enough in a perfect world!
However, we don't live in a perfect world. So you need to model your system more detailledly, think about bandwidths, filters, frequency uncertainty of oscillators.
I'll be a bit blunt, in hopes it helps you find a better question, sorry: you graduated in EE with specializations in RF design. I'd have expected you to ask a more detailed question here with way more background on your overall system! I think you can do better – interference happens only under circumstances where energy of one thing ends up in the other, so maybe you'd want to analyze your proposed system more for the places where that might happen!
That would depend on the bandwidth of the transmission.
The RSGB 'Amateur Radio Band Plans' is a very good reference.
If you want 2 unmodulated finite length sinusoids to be mathematically orthogonal, then the frequency separation is 1/T, where T is the length in time of a DFT used to detect them, and the period of the carriers are an integer submultiple of T. If you want a 3 dB gap between signals or the carriers are not integer periodic in T, then double that separation or a little more. If you use a non-rectangular window, then the separation roughly doubles again. If the channel has an impulse response, then you may need to add a cyclic prefix to cover the multi-path skew, which typically increases T by 25% for a given carrier frequency separation to be orthogonal.