Is there a free database with all geolocations for shorelines?
Is there a free database for near-shore bathymetry data?
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Natural Earth project has these datasets and many more: http://www.naturalearthdata.com/features/
To use the data you could:
All the data uses the standard projection 4326 so no headaches mixing any of the datasets
You could use OpenStreetMap coastlines.
The data is provided by Jochen Topf from here as a shapefile free of charge: https://osmdata.openstreetmap.de/.
Please consider the the ODbL license when working with OpenStreetMap data.