I created a custom object and i want to get all its existing records. Is there a way of doing that via the REST API? Seems like a very basic and simple operation but i couldn't find information about it anywhere.
As you say, it seems like a basic task, but in the reality, it is more complex indeed.
Unfortunately, the Get Custom Object endpoint (which is the only endpoint to fetch Custom Objects) requires the filterType and filterValues parameters to be present as well. Basically this means that you have to have some information about the queried objects beforehand.
Also, a further restriction is that the value of filterType can only be one of the “searchable” fields of the Custom Object, meaning that it has to be either a Link field or a Dedupe field. (These fields are listed under the searchableFields property in the response from the Describe Custom Objects endpoint.)
So as mentioned above, you have to know the values for at least one of the properties of your Custom Objects before you make the query.
With additional queries though, you can grab these required values.
Let's say, you have your Custom Object linked to the Lead Object, and the Link field is called Owner Email (with the REST API name being ownerEmail) which links to the Email Address field of the Lead Object. In this case you could set the filterType to ownerEmail and set the emails of the leads as filterValues.
Then it is up to you how you gather the emails of those Leads who has a Custom Object attached. Luckily the REST API won’t throw an error if you provide a value that has no corresponding Custom Objects.