I do not know how possible it would be for those companies will not do manipulation that you are talking about. I mean in a way they will provide more ETF shares to their customers than the real bitcoin that they bought. But I think the amount of bitcoin they hold to provide bitcoin ETF shares will be transparent for people to see, but I do not know how people will verify the total amount of shares they created from it to be 1:1.

But about the second question. Trading the ETF directly will not have effect on bitcoin price, what will have effect on bitcoin price is if more people are buying the ETF shares and then the company that are providing it are buying more bitcoin when there is need as more people are demanding for the ETF. As the company buy and hold more bitcoin, it will make bitcoin scarce and the demand also will make the price of bitcoin to increase.