1. There's a lot more to websites than just the shopping cart and some sites don't have a cart (or anything similar) so I'd say the answer is no. You could use the cart as the starting point but there's a lot more you'd have to add.
2. If you use someone else's code then you have to abide by their terms and conditions. They automatically get copyright on anything they create, just as you do, and they can sue you if you have copied their code (just as the Tolkien estate could sue you if you copied Lord of the Rings and started passing it off as your own work). Using someone else's code is NOT the same thing as writing the code to do the same sort of thing from scratch and you may have heard about "clean room implementations" - that is where, say, AMD wrote their implementation of Intel's x86 assembly language.
Yes it is a lot easier but you may have to pay them fees for using the results of their labour. Not everyone works for free.