I can't give you a categorical answer on the LCX, but perhaps someone else on here can. You can almost certainly get a map of some sort to show on there, either by exporting directly from RM in AT5 or LCM format, or by exporting Shapefiles from RM and running them through the Navico IMC tool with a lower Atlas version (e.g. 7). If none of that makes any sense to you, don't worry - I can elaborate if required.
In answer to your other questions:
Yes, you can use US or metric units.
RM will work very well with your HDS Gen 2.
RM can export maps and trails to Google Earth, Shapefiles, CSV files and more, so you should be able to get your data into just about any GIS app that you want.