I will make cd layout designs for music albums

No. I can lay out your already existing art and maybe do some little modifications to it if required, but not drawing something from scratch.

Most Cassette/CD/Vinyl factories, if not all, have their own printing templates which they use for cutting the prints precisely. This means if we use a different one it might not have the exact dimensions required and result in an inaccurate print or an extra charge from the factory for fixing it.

Yes and no. I can lay out the art into another template or prepare one (if, for example, you are printing it yourself). But in the end if you are ordering from a pressing plant they will most likely request moving the graphics to their template or charge you some extra money for doing it themselves.