Which of the following orders regarding relative stability of free radicals is correct?

The correct order of stability of the given carbocations is:

Taking into account the stability of various carbocations and the rules governing mechanisms of carbocation rearrangements,which reaction is most likely to occur during the given reaction?

In which of the following reactions does a rearrangement take place with a change in the carbon skeleton?

Most stable carbocation among the following is:

State True or False for the following statements:
$(i)$ $\mathop{C}\limits^{+}H_3$ and $CH_3\mathop{C}\limits^{+}H_2$ both are primary carbocations.
$(ii)$ $(CH_3)_3\mathop{C}\limits^{+}$ is a tertiary carbocation and all carbons are $sp^3$ hybridized.
$(iii)$ $\mathop{C}\limits^{+}H_3$ is trigonal planar.
$(iv)$ $CH_4$ is not trigonal planar.