If a PATCH request is applied to a resource that doesn't exist yet, is it then allowed to create the resource or do I need a separate POST/PUT request in that case?
The PATCH request would go to the URL for the resource for example: PATCH /object/1234. If the object with the ID 1234 is in the database I'll create it, otherwise I'll update it.
The PATCH request doesn't contain all fields, that's why I don't use PUT.
On
Whilst a server can create a new resource (as explained in Heiko's answer), you'd be advised to only implement conditional PATCH, where a client sends an If-Unmodified-Since or If-Match header, ensuring the patch is applied only to the version of the resource the client thought they were editing. Conditional PATCH requests preclude the idea of editing a non-extant resource. If a client attempts to send a request without a precondition, the correct response is 428 Precondition Required. See RFC 6585.
RFC 5789 states that PATCH should be used "to modify an existing HTTP resource." It would probably be best to implement a POST/PUT request in order to adhere to the HTTP standards.