I am new to the OpenStreetMap Api, so sorry for my basic questions: How can I get the geographic coordinates of a city given its name, using the OpenStreetMap API ? And linked to this, how can I retrieve coordinates of streets in this city ?
Thanks !
There's no way to do that using the main api, nor should you be trying to as the main api is intended primarily for editors.
What you want is the geocoder, Nominatim. You can find details of that on the wiki but basically you want to use a query like this:
http://nominatim.openstreetmap.org/search?q=paris&format=xml
Which will return an XML document listing possible matches and their locations.