IOS – Podcasts that I have played or marked as played on the iPhone are not showing as played when I sync to iTunes and are not being removed

I definitely feel your pain when dealing with managing podcasts with iTunes on iOS devices. With the challenges of either creating a smart playlist that I can't then order (at least I've generally found this to be impossible) or the idea of having to micromanage my podcasts through a standard playlist as well as the oddities of what podcasts get synced and why I've generally given up.

What I recommend is a specific podcasting app. There are a few out there. I started with Instacast, but it became a little unstable for me recently. I've since gone to Podcaster, and aside from the initial learning curve, I like it more. The nice thing about either of them is that you never have to use iTunes to sync your podcasts either, as they'll download them over wifi or 3G.

Sorry that I can't provide a solution directly related to your iTunes challenge, but I've been happier going this route and maybe you would be as well.

Your list holds the answer, specifically #4. The problem is the fact that when iTunes it prevented from automatically opening when a device is connected, there's a whole list of actions that simply don't happen, sync triggering is one of them.

Re-enable 'Open iTunes when this iPhone/iPad is connected' and your syncs should work normally, and automatically, again.