I may have found some evidence of trains running to Bender-2
here. It's a YouTube video entitled "Diesel train D1-709 on the route Bender 2 - Chisinau" - although I cannot find any evidence for these D1 trains actually serving Transnistria. I suspect that there's some local politics at play here, as there's plenty of videos showing freight trains arriving in Bender-2, but nothing showing any D1 passenger trains arriving.
With other evidence showing that Moldova has talked about the *possibility* of serving Bender-2 or Tiraspol, it makes me think that these trains have never actually reached Bender-2. I think you're right that the train shown is the Odessa train, which is known to serve Bender-2. So, I suspect this is possibly a political thing in the Chisinau-1 station by showing Bender-2 as the destination, although the train doesn't actually reach there. If you look in the online timetables on the Moldovan Railways website, Bender-3 is served by a completely different train to Bender-1.
So, as far as I can work out: domestic services operate from Chisinau-1 to Bender-3 via Chisinau-3, while international services go from Chisinau-1 to Bender-2 without stopping at Bender-3 or Chisinau-3.
The whole thing seems rather silly, especially as
the border is wide open anyway.
But if they are able to run to Bender 2 it makes me wonder why they do not extend it the short distance to Tiraspol which is the major city.
It all seems very strange there. There's nothing preventing them from running services to/from Tiraspol, and there's at least one book on Google that states that (after the war) multiple trains were running from Tiraspol/Bender to Chisinau and back without problems.
In terms of Chisinau-2 - is it possible that it's in use for freight purposes? It would explain the platforms and the lack of any sign of passenger use.