Such simulated spectra are never completely precise: dynamics of your molecule (i.e. conformational changes on the NMR time scale) are completely neglected and interactions with the surrounding medium (solvent molecules) are either not taken into account at all or massively simplified.

In addition, the computational methods used also include a number of approximations to make the computations handable in the first place.

Vibrational frequencies tend to be too high when calculated in the harmonic approximation. Because of this it is conventional to scale calculated frequencies, by 0.97 or so... NMR is harder to explain, but you should not expect too good of an agreement, calculating NMR accurately is difficult. In your case, you seem to be neglecting the effect of the surrounding medium. Try using a polarisation model. Also, be careful with that basis set. Using diffuse basis functions can cause problems.

Because, the experiments are generally performed on the solid phase and theoretical calculations are performed in gaseous phase.

Also, the harmonic approximation in the vibrational frequency ignores the anharmonic modes. However, it is possible to calculate the vibrational modes including anharmonic modes. In the case of NMR, chemical shielding of the molecule in the solution form and chemical shielding calculated using GIAO can not be compared exactly. One could get the pattern and tentatively assign the experimental NMR peaks using theoretical chemical shifts.

For stretching frequencies, the force constant is computed at the bottom of the potential well. This is where the quadratic form of the potential (i.e., the harmonic oscillator) and the Morse Potential match up. As you will note, the experimental frequency is based on a transition between two vibrational states and will be a lower frequency than the harmonic frequency that fits at the bottom of the Morse potential. For stretching, the experimental frequency includes the anharmonic term which must be a negative term in the Morse potential expansion. Another way of saying the same thing is to take two experimental frequencies and use the appropriate Morse potential expression and solve for the anharmonic and the harmonic terms and you will see the harmonic term is always higher, which is in accord with the harmonic oscillator potential. Remember, the optimized structure locate the minimum energy (and therefore the optimized position) for each mode of the oscillating molecule. That is where the force is zero (1st derivative of the energy = force = 0 at energy minimum) and the second derivative of the energy is equal to the force constant. Hopefully, this makes sense to you.

As for NMR, I have no idea since the isotropic average sigma is based on the cross derivative of the energy with respect to the magnetic field and the nuclear dipole. Maybe there is some simple model out there that gives that insight but I have never looked it up.

Because there in no environmental effects with the calculations by program. I think like an ideal cases.