Rei is the spirit with which we pay respect to the opponent, and the protocols of etiquette through which we express this sentiment is called Reiho. The spirit of Rei serves as a system to preserve social order, and Reiho are the protocols that represent it.
Ukemi is about receiving the fall gracefully. In judo, and life, this is important so that you can rise up to continue the struggle. We learn that you can benefit from the lesson of the fall rather than suffer from it.
Katame-waza refers to the Ne waza (ground techniques) which are applied while the opponent is lying on the floor, as opposed to Tachi-waza (standing techniques) which are applied from a standing posture.
Nage waza includes all techniques in which tori attempts to throw or trip uke, usually with the aim of placing uke on his back. Each technique has three distinct stages: Kuzushi, Tsukuri, and Kake.