I don't believe we ever see it do we? The shot of him walking toward the emperor on the Star Destroyer as they watch the Death Star construction is from behind, so I don't think we ever see it. Can someone confirm?
Trying to see if there is any BTS pics of Hayden walking around in the suit. This one seems to be from Vader coming off the table where it would make sense he wouldn't have a lightsaber. It looks like the table is behind them: This one might, and I emphasize might, be from the Star Destroyer Scene because of the green screen (the above scene from the table used green screen). It seems that if this was from the Star Destroyer scene there is no saber hilt on his belt. Again, this might not be the Star Destroyer scene because it might be a re-shoot or pick up of the table scene just using green screen.... However, there were these produciton photos for ROTS that show Vader holding what appears to be his ANH Saber... So possibly yes he has it when he appears on the Star Destroyer, possibly no...
One of the Darth Vader stories described Vader looking at Sidious's saber as a model for his own, and he considered it an antique. His saber was basically a power tool. Dark Lord: The Rise of Darth Vader takes place shortly after ROTS, and so he must have made his saber within a week or so of his transformation into a cyborg. Not sure if he had it on the Star Destroyer, but he might have. I imagine that takes place a week or so after his transformation. He's walking a bit more slowly than we see him in the CT, which makes sense, given that Dark Lord detailed him struggling with his suit initially.
No. Anakin used his blue lightsaber throughout "Revenge of the Sith", until Obi-Wan took it from him after their Mustafar duel.
I'm not a Lightsaber hilt expert, but from what I know they did design and construct a Vader saber that differed in details from the ANH-ROTJ hilts, which was ultimately exclusively used for promotional images.
Although a lightsaber hilt based on a ROTJ Barbican one was built for the film (see the pic of a Master Replicas ROTS saber in comparison with a real Barbican one and check link below), I believe it was only used for publicity photos like the one mikeximus has posted. http://registry.rebelscum.com/index.php?action=review&review=vader_rots
I am trying to edit my post and I don't know why but I can't do it. Anyway, Barbican Vader saber was used while filming ESB and not ROTJ.
No. I would assume Palpatine gave him the red lightsaber when Vader recovered from his injuries and was starting to hunt the Jedi down.
Vader does not construct his saber until after ROTS. A prop was only made for publicity photos and promotional ventures.
I dont remember seeing him use a red saber until Episode 4, but he may have had his new saber at the end of 3.
Uh, no. Look at those photos. Hayden didn't wear it at all in ROTS. As you can see here in ANH, the saber is on his left side as normal. It is not there in ROTS.
Is anyone curious to know the origin of the armor. Was it ever worn by any of Palpatine's pawns? I wonder if it was built just as Vader was being operated on? That might be the case and the most realistic way to never explain it but I think it would be cool if Vader's armor was worn by others besides Anakin.