In which of the following species is the central $C$-atom negatively charged?

The reaction of methyltrichloroacetate $(Cl_{3}CCO_{2}Me)$ with sodium methoxide $(NaOMe)$ generates

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.

Which of the following carbocations will undergo rearrangement?

What is the hybridization state of a carbocation?

Which of the following carbocations is expected to be most stable?