How uncertainty principle can be used to calculate the range of actual variables

I know the uncertainty relation $Delta x Delta p ge frac{hbar}{2}$ tells the uncertainty in position and momentum, or energy and time should be greater than or equal to $frac{hbar}{2}$, but I don’t understand how this relation can be used to give an estimation on size of system or energy of system.

i.e. When we want to prove that an electron cannot remain inside the nucleus, we use this formula and put the size of nucleus (femtometers) in it and get energy(using momentum calculated from the relation) of electron which contradicts the actual value measured in the experiment, so we conclude that electron cannot reside in the nucleus.

Also we use energy-time uncertainty relation to calculate the time range of exchange particles using their energy values, but I don’t understand how we can do that since uncertainty relation only tells about the uncertainty in variables and not anything about their typical values?

A similar type of question is asked here Why the uncertainty principle can be used for estimation?
but no satisfactory answer is provided