Are we so sure that senators are democratically elected?
For the most part I'd say they were appointed, not elected. In practical terms they're closer to UN Ambassadors than Senators in that they're representing a government, not the constituents directly. Even so I'm pretty sure the appointment of a Senator is up to the government of each system/sector constituency to determine; though election or appointment, I don't think the Republic Senate itself care how they get there, so long as the post is filled.
FWIW I'm pretty sure AotC states that Amidala was asked to take up the post of Senator by the new Queen; not something she ran a campaign for.
"When I left you..." is always taken to literally. It could mean when he left the Jedi and became a Sith not when he last physically parted ways with Obi-Wan
This is one of those lines that's been given way more weight than it warrants.
In it's original context, Vader was
"a pupil of [Ben's], until he turned to evil", so the clear intent was in reference to when he left Kenobi's tutelage, whenever that was.
As things stand now, I see no reason why it has to be any different; as in it refers to when Anakin was Knighted. "Leaving" him as in no longer his apprentice, which is more literal than one might think since Padawans basically live with their Masters. They may have their own chambers while at the temple, but most of their time is spent at their Master's side. That's kind of how historical apprenticeships worked.
Yes he saw Obi-Wan all the time and worked
with him a lot during the Clone Wars, but that's akin to still seeing your parents/family regularly after going off to college and beyond. One doesn't have to be completely separated, never to interact again to have "left".
Once Knighted, Anakin was his own person . . . for about eight months, then Yoda lumbered him with a padawan to follow him around wherever he went. Of course her "leaving" was way more absolute, but it was a very different situation.