Yes they do. That's why runs on banks are a problem. Only the central bank (at least in the US) creates money. And you can't invest your money in the central bank.
When a US bank approves you for a loan, it simply credits your account with new money. This money does not come from other accounts, i.e. this "investment" in you is made entirely with new money, created by the bank. When you repay the loan, the money disappears from the system.
There are limits to how much money can be created in this way, but those aren't relevant here.
You are correct. Fractional reserve banking is a myth . Banks do not lend out deposits. Deposits come from loans. Reserve requirements do exist but they do no limit bank lending. Lending is only limited by demand for loans and capital requirements.
Here is a pretty good site which explains how the banking system actually operates in detail.
I didn't downvote, but the parent is conflating money with credit. Banks and other lenders create credit. Only the Fed creates money. When credit starts to contract and economic growth isn't strong enough to sustain increased creation of money you get a deleveraging, as we recently experienced.
So yes, in one sense banks do create "money", but what you're calling money is actually credit.
That's not "creating" money - you have "money" in your account, but that's just a number. In reality, that money is on the bank's balance sheet, and it can lend it to others (or a part of it, depending on the regulations). It can also lend money that was actually created by the central bank and loaned to the commercial bank. But regardless of the number on your account, if the bank runs out of money (is insolvent), your money is gone (absent government guarantees/bailouts).
You are confused. There is no such thing as a loanable funds market. The guy at the bank making the loan does not call the other guy at the bank to look in the safe and see if the funds exist to loan out. Doesn't work that way. Banks have to have appropriate capital ratios in order to stay in business and be considered solvent. Those ratios are entirely determined by regulation. By and large, the only thing stopping a bank from 'creating money' or making a loan is the willing and able consumers.
Yes they do. That's why runs on banks are a problem. Only the central bank (at least in the US) creates money. And you can't invest your money in the central bank.