Lyon is one of three largest cities of France.
There's a widely used public bicycle system. You need a bank card and probably some payment. Then the first hour of using a bicycle is free.
Metro with a glass door at the entrance. A single ticket costs 1.80 EUR and is valid for 1 hour for all the transport.
black riding works with the metro, just go in quickly after someone. Control may be dressed in civil. On bus and tram controls are quite frequent. Alternatively look for used tickets left around by people. The tickets can be used up to an hour after they were validated. Tickets also work for all public transport in the city.
The parks on Fourvière Hill in Vieux Lyon are peaceful at night and if you are too, no one will bother you for camping out there. It's nearby, but it feels so far outside of the city that you can get a relaxing night of sleep without worrying about police or thieves. It is however quite difficult to find a flat place there. The park I slept in is called "La Sarra". You should see the name on your phone maps. However I recommend you to go and check out the park a bit earlier since it could be locked at night. If you don't have other options you can spend the night in Part-Dieu shopping center. Surveillance staff don't bother you if mantain a low-profile.
Free showers at Bains Douches in the 1st (metro Croix Paquet) and 7th (metro Debourg) arrondissement. Closed on tuesday afternoon, saturday and sunday. Staff give you soap and towel if you need.
Edit July 2017: Couldn't find the showers in the Croix Paquet, so I went to the metro Debourg district. The address is: 13 Rue Benjamin Delessert
Check trashwiki. Get up early and go in the morning! (check trashwiki for specific info.) There is a lot the city has to offer in those few hours when the bins are outside. Franprix shops have nice things in bins.
Shopping centre Part-Dieu near train station has a sitting place in the bottom floor with many electric plugs and wifi (which you can catch from nearby mcdonalds). There were already many people sitting and using their devices.
You can have free access to internet in public libraries. Near Gare Part-Dieu - central railway station - (exit on the eastside) there's a shopping mall called La Part-Dieu that offers free and unlimited wi-fi. Next to the left of this shopping center Bibliotheque Municipale de Lyon offers free internet, too.
Busking in Lyon is possible. Police seems to be not bothering anybody. During weekends it's quite crowded around Place de la Republique and Place Bellecour. It's the city centre and shopping street and there are already some local buskers - but in April 2016 the competition doesn't seem too big. A place Terreux is a good spot, too. People were suggesting old town and some terraces with view. Untested.
The earnings are average (very subjective observation).