Is there a way to access to the mempool through RPC API? And is there a way to manipulate the mempool from the outside?
You can view the mempool via this RPC API endpoint.
You currently can't manipulate the mempool with the RPC API. You can change the mempool filter settings though (which are used to filter out operations based on min fee requirements).
I noticed that
/chains/<chain_id>/mempool/pending_operations is not described anywhere in the official documentation.