While not a solution right now, I just want to add that the general transit feed spec aims to solve the data interoperability of different transit systems. The transit system keeps a publicly accessible zip file up to date, and then anyone can pull/parse the schedule/prediction data in a consistent way across transit systems. I know in the us adoption is slow, with vendors prefering to build their own walled gardens and transit agencies lacking the vocabulary or skills to advocate for more open data/tools
Transportr if you want detailed departure and arrival times.
OrganicMaps for Google Maps replacement, lets you choose to route as pedestrian, via car or public transport (but only shows you one option and no departure times).
I recently moved from osmand to organic maps (now that they add gpx support) and even if it cannot be compared to gmaps it's the most usable and have metro maps in it