Can I connect a cable NYBY Flame retardant armored cable with a NYY non-armored cable by means of a joint 4ПСТ-1? The voltage is 1000 V.

It is possible to connect an armored cable with a non-armored one. Uncoat the cable, armoring straps should be cut till the edge of the outer coating of the cable. Earthing of the armoring straps is possible only at one side- in the termination. It is better to use termination 4ПСТнг-LS-1, as it is also flame retardant like the cables that you mentioned. If there are no strict requirements for flame retardance, then you can use the termination 4ПСТ-1.