Create a calendar to launch a query on the attributes concerned by the selected date. Windows type calendar, month displayed with two forward/backward arrows to change month. Is it possible to link this type of "window" with a query?

I'm not sure if I understand your question correctly, but you could create a lookup table where you map a date to a query.

Like above, I'm not exactly sure what you're asking. If you're looking to build a tool to be accessed in ArcMap (Preferably ArcGIS Pro as ArcMap is very close to retirement) You'll need to look at ArcObjects (https://support.esri.com/en-us/products/arcobjects-sdk) or you may be able to do what you want to do with the Interoperability extension (https://www.esri.com/en-us/arcgis/products/arcgis-data-interoperability/overview) which is FME embedded in ArcGIS

Thank you for your answers, you have already given me some ideas.

I actually work on ArcGis.

More precisely, I would like to have a calendar interface like the one below for example and each time I select a date, the objects entered on that date would be highlighted. Clicking on the date launches the query "searches for objects with this entry date as an attribute".

This would allow me to run queries on dates with a click without using the ArcGis query tool, is this possible?

Thank you for your answers.

You'd have to build this as a custom extension with the ArcObjects Framework.

You could have an FME process that you run, and outputs a separate dataset that you can then add into ArcMap. FME isn't able to control the ArcMap interface and select features on the map