I have an account where I am buying monthly a MSCI World ETF. I am now thinking about adding to this account single shares from a few different companies. What impact could this have if I mix up my depot with ETF's and Shares? Or is there no effect at all?
What you have is an investment account, with ETF in it.
(In America, at least, retail and commercial banks can't offer investments, though they do "partner" or merge with investment banks that do offer this service, so that you can see both checking and savings accounts and investment accounts in one place.)
As for the heart of your question, "What impact could this have if I mix up my depot with ETF's and Shares? Or is there no effect at all?" the technical answer is: no effect at all.
Note, though, that while ETFs and mutual funds are "designed" for buy and hold, many people tend to get "happy feet" with individual stocks, selling and buying at the wrong times.
So... first "know yourself"!