1) gchar* gweather_info_get_forecast() was removed in https://git.gnome.org/browse/libgweather/commit/?id=2e3ae2b410af07c7eedb7ef16dce684d012a80f8 and superseded by GSList* gweather_info_get_forecast_list(). 
Both functions have been available at least since 3.6, see https://developer.gnome.org/libgweather/3.6/libgweather-GWeatherInfo.html#gweather-info-get-forecast

make[4]: Entering directory `/run/media/andre/linux/git/gnome/evolution-data-server/calendar/backends/weather'
e-cal-backend-weather.c: In function 'create_weather':
e-cal-backend-weather.c:438:2: warning: 'gweather_info_get_forecast' is deprecated (declared at /run/media/andre/linux/builds/gnome/include/libgweather-3.0/libgweather/gweather-weather.h:102): Use 'gweather_info_get_forecast_list' instead [-Wdeprecated-declarations]
  tmp = gweather_info_get_forecast (report);
  ^


2) GWeatherLocation* gweather_location_new_world(): https://developer.gnome.org/libgweather/3.6/GWeatherLocation.html#gweather-location-new-world
was removed for 3.10 in https://git.gnome.org/browse/libgweather/commit/?id=d5332e605a297f4ec402ea323946193962a4ed33 by replacing it by
GWeatherLocation* gweather_location_get_world() since 3.10:
https://developer.gnome.org/libgweather/3.10/GWeatherLocation.html#gweather-location-get-world

e-weather-source.c: In function 'e_weather_source_new':
e-weather-source.c:124:2: warning: 'gweather_location_new_world' is deprecated (declared at /run/media/andre/linux/builds/gnome/include/libgweather-3.0/libgweather/gweather-location.h:54): Use 'gweather_location_get_world' instead [-Wdeprecated-declarations]
  world = gweather_location_new_world (FALSE);
  ^
make[4]: Leaving directory `/run/media/andre/linux/git/gnome/evolution-data-server/calendar/backends/weather'