"can anyone please explain if there is a direct relationship between camera frame size, lens focal length and field of view?" Yes there is... but I can't explain it off the top of my head.
FOV is the most useful description but you rarely see it mentioned.
As far as I know there are 4 Canon and 2 Nikon full frame cameras on the market. They have sensors that are nearly 36x24mm.
Here's an illustration from wiki:
The full frame sensors are nearly 36x24mm but not exact... so the framing is not exactly like 35mm film but it's darn near exact.
The cameras that use the so called 1.6x factor use the ASP-C size sensors shown above.
Some cameras like the original Canon 5D have a viewfinder that crops off some of what you actually get in your photo. You don't see the full Field of View... but it's there on the photo.
There are Field of View calculators out there on the internet, they were once very common in Video because it was common to use a so called 2/3" chip lens on a 1/2" or 1/3" chip camera and it was useful to correlate, as your are trying to do, the field of view to the specified focal length.
The relation ship between focal length, aperture, back focus, and imaging area is pretty universal... I had to think through the same things when I bought my telescope and selected the eye pieces... as the field of view is the result of all the other circumstances.
Anyways, you are on the right track and thinking about the consequences of the chip size correctly.
I suggest you search out a online calculator to make better sense of how the focal length yields varying FOV with different image areas.
Merry Christmas.
best regards,
mike