Is it true To obtain a 20 mM Tris-HCl pH 7.4 solution, I just need to dilute 2 mL of 1 M Tris-HCl pH 7.4 to 98 mL of nuclease-free water (Total Volume 100mL)
It is the correct dilution, but bear in mind that the pH may shift a little upon dilution of the concentrated stock solution. If it is critical that the pH be 7.4, you should measure the final pH with a Tris-compatible pH electrode and adjust the pH as necessary with NaCl or NaOH.
Yes, that's right. Just re-check the pH, before finalising the volume. De-ionised water should not affect the pH, but it tends to absorb CO2 during storage, which can lower the pH slightly, although it has no buffering ability in itself.