Assuming you have two full 20lb tanks, no issue with going 7 days with fridge, cooking, and hot water.
Difficult to provide a solid answer on the battery usage and charging without a lot more details on battery(ies), charging panel size, exposure (sun vs. shade), number of lights, number of times the awning will go in and out, water pump usage, etc. Generally, LED lights are not much of an issue. The biggest draw on the battery will be the furnace motor.
Be careful to not run the battery down to low as it will impact the refrigerator. It requires 12V for its control board. A digital volt meter will allow you to monitor the battery health and adjust usage as required.