Rotating a molecule or atoms about a specific bond does not result in different isomers. The result is the exact same molecule that you started with! The key with isomers is actually arranging the atoms in different places within the molecule.

In addition, structural isomers can arise from molecules that have carbon double-bonds, but it is not limited to them. That would lead me to choose the first statement in your query as false.

The second statement makes sense. Think about it: if the carbon skeleton increases in size, that means that you have more carbon atoms that are available to bond with other atoms. The more different atoms, the more possible arrangements for them.

You may find this website helpful:

http://www.chemguide.co.uk/basicorg/isomerism/structural.html