I've inherited an account and every field and every object object in Sales Cloud has been set to sync into synchronised DEs in Marketing Cloud via the connector. Some of the objects have hundreds of fields or are no longer used very much. I didn't set the connector up, so is it possible to only bring some objects over via the connector, and only some fields within each object, or does it have to bring everything over? If it's possible to set it to some objects/fields, where do I configure this?
It for sure is not a requirement to sync every single object and field. I will refrain from removing too many objects without validating which of them are used in e.g. Query Activities. You will see, that some of the objects are prerequisites for having others synced. E.g. User object needs to be synced prior to syncing much else - even though I tend to never use it.
You want to visit Synchronised Data Sources, under Contact Builder, to adjust the synchronisation settings:
Here you can click on one of the objects to adjust the settings:
Or Set Up Object (probably not relevant for you) to add another object to synchronisation.