organic chemistry - What is the geometry of an alkyl radical?

I encountered this question which asks how many possible radicals are formed when $\ce{CH3CH2C(CH3)3}$ is monosubstituted by $\ce{Br2}$. The answer given is 3 while I think it should be 4, reasoning that there is a "chiral" carbon if the radical is formed on carbon 3. While arguing with my tutor two questions came to my mind:

1. What is the geometry of the $\ce{CH3\dot{\ce{C}}HC(CH3)3}$ radical?


2. If the radical is trigonal pyramidal, does it transition quickly between the two possible states? If so are they considered two radicals?

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My findings so far:

This answer on SE hints that the exact shape depends on the substituents on the alkyl radical.

Modern Physical Organic Chemistry states that all other (non-methyl) localized radicals are not planar.

Organic Reaction Mechanisms states that the geometry of free radicals is still controversial.