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1. why on earth would my hand be folded as last to act when it's checked to me?

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Simple: because doing otherwise would slow the table down for the other players. They're not going to let you take 30 seconds every round until you get reconnected again, and rightly so.

And it sounds like you were playing at a table with no disconnect protection (clearly marked "No DP," and you have to click OK to a box telling you there's no DP when you sit down), or that you used up your quota. If you used up your quota, you might consider changing your ISP.

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2. party is insisting there were no connection problems and is refusing to either give me that pot or at least return my bets

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Party Poker disconnection policy

You agreed to this when you signed up.

HTH.