You want to query metadata? Names of available tables, names of columns you can see in each table, maybe types instead of real Account/Contact/... data, correct?
You might have to bump the version of the API up a bit, current is 47 / 48 so some objects might not be visible in your current one. Also - what API options you have? SOAP, REST? Is "Tooling API" an option? Because it has very nice official FieldDefinition
table to pull this.
It's not perfect but this could get you started:
SELECT EntityDefinition.QualifiedApiName, QualifiedApiName, DataType
FROM FieldDefinition
WHERE EntityDefinition.QualifiedApiName IN ('Account', 'Contact', 'myNamespace__myCustomObject__c')
I don't see the table in the REST API reference but it seems to query OK in Workbench so there's hope.
Generally try to Google around about EntityDefinition, FieldDefinition, EntityParticle... For example this is a decent shot at learning which tables are visible to you:
SELECT KeyPrefix, QualifiedApiName, Label, IsQueryable, IsDeprecatedAndHidden, IsCustomSetting
FROM EntityDefinition
WHERE IsCustomizable = true AND IsCustomSetting = false
Or in a pinch you could try to see which fields your user has permission to query. It's bit roundabout way to do it but I have no idea which tables your connector can "see".