Edits are stored localy on your phone/tablet, and sent to osm (along with GPS traces you could have recorded) when you manually hit "send data" while a connection is available
I could have sworn I saw an EFF (?) link back in June (post-Snowden) containing a list of FOSS alternatives to a bunch of services (Gmail, Skype, Google Analytics), etc. For some reason I can't find it now, though - hopefully someone else has this saved somewhere.
You can already do that.
Routing is in the works (see https://github.com/openstreetmap/openstreetmap-website/issue...). For now you can use http://map.project-osrm.org/ but having it in plain sight on osm.org will definitely be better