In which case does the heterolysis of the carbon-chlorine bond lead to the most stable carbocation?

The stability of the following carbanions is in the order of:

Explain why $((CH_3)_3C)^+$ is more stable than $(CH_3CH_2)^+$ and $(CH_3)^+$ is the least stable carbocation.

The geometry of the reaction intermediate in an $S_N1$ reaction is:

Which of the following intermediates is not expected to be formed in the following reaction?

Given below are two statements:
Statement $I$: $(CH_3)_3C^{+}$ is more stable than $CH_3^{+}$ as nine hyperconjugation interactions are possible in $(CH_3)_3C^{+}$.
Statement $II$: $CH_3^{+}$ is less stable than $(CH_3)_3C^{+}$ as only three hyperconjugation interactions are possible in $CH_3^{+}$.
In the light of the above statements, choose the correct answer from the options given below.