What type bat. lead acid or AGM, how to replace

Thanks to all who post here, I've learned how to change oil to changing front brakes. At first I was hesitant to even touch my wife's 1009 BMW 128i but after reading this I felt better.



Now, I've been reading about AGM batteries and I thought those were in all BMW but when I contacted the dealer he thinks my car has an lead acid bat. He also said a battery replacement will be $425-475 and another $125 to register. He actually stuttered trying to explain.



I can buy one from Auto Zone for $150-175 lead acid or AGM and I've read to attach either a charger or another jumper car to the terminals under the hood. Then remove the battery, but the battery has a big red thing over the positive terminal, how is that removed. I think I've read that there is a switch in the red block?



Also there is a little BMW shop a few miles from the house who will register it for $50



Sorry for the long post.



Thanks

David