Final answer:
The third isomer of C5H12, aside from pentane (n-pentane) and 2-methylbutane, is 2,2-dimethylpropane. The other structures are not isomers due to incorrect bonding or representing the same molecule as an existing isomer.
Step-by-step explanation:
The third isomer of C5H12 that you are looking for, not including pentane (n-pentane) and 2-methylbutane, is 2,2-dimethylpropane. The structures you have proposed either represent the same molecule as pentane or they don't follow the rules of chemical structure (for example, all carbons must have four bonds, including those with hydrogen).
Concerning your first structure, if we add the removed hydrogens back, it is the same as pentane (n-pentane). Your second structure is unclear because it doesn't show where the hydrogens would be, and carbons seem to be forming bonds with too many other carbons; remember each carbon should have four bonds overall.
The structures numbered 3-6 are not possible isomers of C5H12 due to incorrect bonding (like having a carbon bonded to five other atoms which is not possible for single covalent bonds).
As for the confirmational isomerism due to bond rotation, you're correct that the rotation around single bonds (sigma bonds) can make molecules look different, but that doesn't change their connectivity and hence does not result in a different isomer.
Finally, 2,2-dimethylpropane is the correct third isomer of C5H12. It differs from pentane and 2-methylbutane in the way the carbon atoms are arranged: it has a central carbon atom with four methyl groups attached.