1) I'm not sure about that. I think any pre-market activity influences the price it trades at during the day. For example, if a stock goes up 10% up pre-market because it beats earnings, it usually stays at that price level during the day. Just because people see the price up in pre-market. Same if it goes down. It acts as some sort of marker. It would be interesting to see how prices would be impacted if there were absolutely zero pre-market activity. For instance, if $SPY didn't drop 10% pre-market, and nobody put in any bids/sells yet, would $SPY open at 10% down? If it goes down even more, then so be it. At least, that's what the market wants. Not on an arbitrary marker price they see in pre-market and is stuck in their mind.
2) I think short selling helps misprice stocks in both directions. It creates artificial price increases simply b/c of shorts covering as well. Let stocks go up because more people want to buy it than they want to sell. And let stocks go down because more people want to sell than they want to buy. That's what a market is for other assets - whether it's ebay, amazon, groceries, etc. Don't let other technicalities affect the price.