Are exchanges using rehypothecation? Many people think so. It's extremely likely that they are if they are able to. This is why there is always a constant voice to get BTC off of exchanges. The thought is that if everyone withdrew their BTC, the exchanges wouldn't have enough BTC to send everyone and would have to purchase more on the open market. If there isn't enough BTC for sale to fill all of the withdrawals, what happens? Exchanges go bankrupt, the price goes as high as is possible with the funds that are left, and those who held onto their own BTC would be wildly rich.
Does rehypothecation cause a decline in price? Yes. Simple supply and demand. They're creating supply out of thin air that doesn't exist to meet demand instead of allowing the market to correct with a natural price.
With Bitcoin, it would be extremely easy for exchanges to publicly prove their reserves 24/7. Nobody uses Bitcoin for it's transparency though, unfortunately. It's just about hodling and pumping. If any exchange actually cared about Bitcoin, they would give up to the second publicly accessible feeds that showed their customer deposit numbers as well as a list of addresses that hold all their coins. 100% transparency is easy when you're honest.