How can you check the projection of your shapefile in QGIS before and after reprojecting it?

Three paragraphs in is a strange place to finally introduce what QGIS is. That should have been introduced at the beginning, along with a link to their homepage.

Alternatively you can use the 'Reproject Layer' tool. This would be a much better approach if you need to batch reproject several layers of data. It also would be useful to incorporate into a model, where it is important that of your data is in a consistent projection.

To reproject a shapefile in QGIS, you can use the "Save As" option: Right-click on the layer in the Layers Panel. Select "Export" > "Save As..." In the "Save vector layer as" dialog, choose the desired CRS under the "CRS" section. Specify the output file format and location. Click "OK" to reproject and save the shapefile with the new projection.

Depending on your specific requirements, you can also use the reproject tool in the vector toolbox. This would eliminate generating an entirely new file.

Okay, taking the risk to be named a purist, but... I wouldn't call WGS 84 a projection. It is a geographic coordinate reference system in my view. The described projection (the Google Maps one) is the Spherical Mercator/WebMercator/Pseudo-Mercator known as EPSG:3857. Otherwise, basically every country has it's own projection, sometimes more, as a decent map of the country was historically indispensable for the rulers of the country. That is why the answer to the question "what are some common projections" will most likely miss out the ones that most people use. In the Netherlands, nearly everyone uses EPSG:28992 (RD New). So for that specific user group that is the most common one. However, cross one border and nobody will use it...

Common projections used in GIS include: Mercator: Suitable for navigation but distorts area and shape. WGS 84 (EPSG:4326): A geographic coordinate system used by GPS. UTM (Universal Transverse Mercator): Divides the Earth into zones for accurate local mapping. Web Mercator (EPSG:3857): Used by web mapping services like Google Maps.

It would be helpful to include the differences between a Geographic Coordinate Reference System and a Projected Coordinate System.

We have to follow projection mainly because of the irregular shape of our earth's surface. This is why we have geographic coordinate systems and projected coordinate systems. Geographic coordinate systems mainly denote the earth as a sphere (like wgs84) where the mathematical models can be easily implemented. But when it comes to the actual scenario, it is no way near to compensate for the actual coordinates of the ground. For that reason, projection of the geographic coordinates is done using number methods so it can represent the actual coordinates on the ground.

It is also important to consult official cartography sources, such as the IBGE in Brazil, the USGS in the United States, and other equivalent agencies in different countries, to ensure that the chosen projections are appropriate and accurate. These agencies provide guidelines and updated data that are essential for cartography and geoprocessing. Additionally, there are websites that provide comprehensive lists of EPSG codes, such as EPSG.io and spatialreference.org, which can be valuable resources for finding and verifying coordinate reference systems.