I would use geotextile under the liner, and liner scraps under the rock 2-3 layers thick. I don't like to put geo fab in the stream as I am not sure how long it will last fully submerged and I have found that multiple layers of 45mil is extremely difficult to puncture and scraps are readily available for rock pads.
That rock looks to be basalt, if so I doubt any normal skidsteer or backhoe will be able to lift it. In my area a crane is $200/hr 2 hour min. Very cool rock though.