Do banks lend out more money than is entrusted to them by depositors?

That should never happen. At least in the US we aim to lend out about 85% to 90% of total assets at the high end. You do want to lend out because the interest you make in return could benefit your depositors with better rates on thier share accounts. At the same time you dont want to put them in high risk.

The short answer is "abslotely never".

As a matter of fact, banks always are lending or investing less than entrusted money deposits, this is in accordance with the monetary authorities regulation whom they are specifically determined the maximum percentage of the total deposits that the bank has and is allowing to lend or invest at any time to protect the depositors money as well as keeping liquidity in the society in a very save position.

Of-course not, if the bank is dealing with a conservative mind system, unless if Banks can lend money from other resources with less interest rate to gain the difference. 

But it will carry an added risk to it`s usual inherent risk

Banks depends on many factors on lending in or out money