Will this work for Briggs and Stratton generator # 01815 with Briggs and Stratton engine # 384445-0112-E1.....??

No, this maintenance kit will not work that specific engine on that standby generator. For your particular engine, you will want to get the following maintenance parts: air filter 841359, pre-filter 272490S, oil filter 492932S, two spark plugs 794903, and you'll need 48 ounces of synthetic 5W-30 oil (if using our our 32 ounce bottles of synthetic 5W-30, you'll need to get two of part number 100074).