How to use GPS without using Google Location Services Because I do not want to consent to the Google Location Services privacy agreement I have this switched off. By doing so I know some location functionality like cell-based and wifi-based location will not be functional.

However I would expect simple GPS functionality to work in a normal way. Functioning in a normal way to me would be to use GPS data if available, else use the last known location. (Historically this is how GPS receivers work)
The current (I am running Android 5, Lollipop) implementation from Google however seems to not give any location at all when there is no clear fix, throwing me lots of warnings and placing me all over the world instead of in my home location. 

My question:
Does anyone know a third party location provider / spoofer which simply caches my last known location if there is no GPS fix? (just giving me back normal functionality)
Additional functionality which would be very welcome is caching Wifi/Cell data so if I have been somewhere it will remember without a GPS fix.

Any suggestions would greatly be appreciated!
Not exactly matching your description (using the "last known" position if not GPS available), but still a good alternative:

On two of my devices, I completely got rid of all proprietary Google services, replacing them by alternatives. In detail, I've described this in Android without Google 5: Free your Droid!¹ (update¹). In short, this is what I've done:


Flash a custom ROM that comes without GApps (here: CyanogenMod)
Installing microG (successor of NOGAPPS)
Generating the lacells.db as described at XDA, and pushed it to the device


As a result, I've got a totally offline working location service using cell tower IDs and the lacells.db, Playstore access via BlankStore¹ or YalpStore, and a working Maps API using OpenStreetMap. So with "no GPS active", I still get my location as long as there are cell towers in reach. I can, however, not say whether it's using the "last known position" if there's no GPS and no cell towers.

¹ Disclosure: link go to one of my sites