Hi,
Maybe we had a misunderstanding in the term disappears.
Do you mean that you create a context, you save and open the catalog then the catalog is not present?
The map at step 2 of the context-editing allows to edit the base map. The tools you want in the final map (included catalog) can be selected on the 3rd step.
Because the catalog can be reached from the List of layers, from the Sidebar or from the Burger Menu), by default the catalog do not bring a container plugin.
You should add "List of layers", "BurgerMenu" to be able to open it.
From "list of layers, the catalog is available from here ("Add Layers")
About the failing requests , the WPS is normal. MapStore tries to find out some services from GeoServer to see if it can activate advanced features.
The other one means that you don't have WFS service available, and for this reason you will not be able to see the Attribute table