Everyone's cancer is different. Stage IV is the highest the stages go. Having brain mets means it has already spread from your lungs to your brain. Some stage IV patients can have surgery because of where the tumors are located, others can not. It is determined case by case, person by person. Get a second opinion. You are totally within your rights to get all the opinions you want. Take a notebook or recorder with you so you can write down the answers. Make sure you write all of your questions down as you think of them. If you can, it's best to have someone go to the appointments with you to help keep track of all the information. Ask your doctor to show you the pictures of your tumors (CT scan and/or MRI images) and explain to you what is what and where it is. The more you know, the more you will understand. My dad's doctors were both happy and a little nervous when they saw me coming because I'd block the door and ask questions repeatedly in different ways to make sure the answers were the same and that my dad understood what the doctor was saying.
I wish you well in your journey. Please feel free to contact me if you want to talk more about anything. (BTW - my kids have paws, too!)