Diastereomers or not
Your first set of compounds are identical.
In the Fischer projection of a chiral centre, you can rotate three of the connected groups in a clockwise/anti-clockwise direction without changing the configuration of the chiral centre.
Upon performing this operation (keeping the top fixed, rotating bottom three clockwise) on the first compound in the first set, we see that the methyl group now occupies the position of the $\ce{-CH3}$ group in the second compound and the $\ce{-CH3}$ in the first occupies the position of the methyl group of the second.
Now, $\ce{-CH3} \equiv -\text{Me}$. Therefore, the first two compounds are now identical. As yukelid stated, identical compounds are not diastereomers.
However, repeating the same for the second case does yield two different compounds that are non-mirror images yet non-superimposable. Hence they are diastereomers.
Enantiomers and diastereomers are only seen for chiral compounds since achiral compounds would have symmetry that makes them identical. So, chirality is needed for enantiomers and diastereomers.