Would this all be fixed by installing a linux distro on the laptop? A different trackpad driver - if it works ;) - would do different stuff, and remapping media keys is possible in most desktop environments.
This doesn't happen to me on an asus zenbook and linux. Two finger scroll works fine, no proprietary drivers installed.
In fact, all the functionality that you generally expect to be broken on linux (two finger scroll, keyboard lights, volume control, etc) worked out of the box...
Yes, it would. This is actually a benefit of Linux (and the BSDs for that matter) - since all drivers are in the main kernel, you don't get as much idiocy from hardware makers that try to do something clever.
It's a gamble though, in my experience Linux support for native device power management is very spotty. You might trade a crappy trackpad driver for no sleep, no CPU throttling, etc.
In fact, all the functionality that you generally expect to be broken on linux (two finger scroll, keyboard lights, volume control, etc) worked out of the box...