In a deflation based economy as invisioned by crypto currency enthusiasts, there is no incentive to lend your money to anybody. Neither a private person nor banks would have strong incentives to do that, because you have a guaranteed increase of value if you just sit on your money.
Nothing. It's just a number in an account. It's what we call money basically.
Banks don't profit from keeping your deposits, they profit from running the money supply which empowers them to create new money which they tax or, in other words, loans on which they charge interest.
Go and try to withdraw something tangible with intrinsic value from a bank and you'll see they don't owe you anything at all. The most you'll get from them is paper, but even then you'll find it withdraw all your money in paper.
I just opened an account for you in my own bank, in fact. You have one million credits. You are free to send and receive credits from anybody else with an account (which is nobody, unfortunately). I owe you nothing.
When was the last time you went to the bank teller and handed them $100 in cash? I haven't done that in well over 20 years now. Notes and coins represent less than 3% of the money supply in countries like the UK and US. It's not what money is any more.
No investments would take place because of that.