LS3 is 6.162 Litres or 376 cubic inches
compression is 10.7:1
I was a Mustang person so I'll let someone with more expertise in bowtie products to discuss headers and the CAI.
In general anything that improves the flow of air into or out of the engine is a benefit...but not all products are created equal
Also remember headers will likely increase peak horsepower but you tend to give up a little torque, you have to balance high flow exhaust with a bit of back pressure.