Question

why n-methyl methylamine is a stronger base than methylamine

Answer 1

N-methylmethanamine is a stronger base than methyl amine.
This is because of the +I effect of the two methyl groups in N-methylmethanamine which increases the electron density on the N-atom making the carbocation intermediate more stable.
In methyl amine, there is only one methyl group. Thus, it has less electron density increase than N-methylmethanamine and hence the carbocation intermediate is less stable.
We know, greater the stability of the intermediate stronger is the base.
Thus, N-methylmethanamine is more stable than methyl amine. (This is the case when the compounds are in gaseous phase)