You have to wonder about someone who leaves a bmw out in the weather like that. Â

Â
I'd think a piece of carpet would be worse than nothing.
Does that mean you're surrounded by more fresh than salt water?
Thankfully these airheads were built with the highest quality aluminum alloy that doesn't pit and corrode away like the Japanese bikes or even the newer beemers. The way to clean yours would be soda blasting or a chemical like ZepALume.
I agree, it was probably already on its way down when parked - I got one that sat out for four or five years, the first couple years covered with a tarp till that disintigrated. It cleaned up and didn't look anywhere near as corroded. It looks to me like the frame and subframe should both be sandblasted and repainted. I'm not a fan of powder coating from the problems with used bikes I've had. The original paint on your bike was rather poor and tended towards rust even when treated well, so don't go with the stock satin or flat black paint - whatever it was. Stock in this case isn't a good idea! Another tedious task is going to be going through all of the electrical connections. I'd get one of the products specifically for that sort of thing - like de-oxit.
If it was me, I'd pull the bike apart, blast the frame and metal bits, repaint, clean the aluminum bits while it's apart and re-assemble. That seems like the best and quickest way to go about it.
I'd also be concerned about the gas tank, especially the  right side without a petcock. Water tends to accumulate and rust the bottom.