Yes you can use the barrel. The inch barrels have the shoulder set back just a little bit to allow for the use of a washer. If everything is correct generally you can put a metric barrel on an inch receiver and use no breaching washer. As you are finding out though if you put a inch barrel on a metric receiver, but you'll need the breaching washer. You have to use whatever gas system the barrel is though.
In the bottom photo the receiver is missing the locking shoulder. That is what the back of the bolt rests against to stop rearward movent and it sets your headspace so they are available in different sizes.