2) In the UK, most machines make you take the card out before dispensing the banknotes. Bank-owned (non-corner-shop) ATMs "spit out" the card and beep until you take the card. Only then do they dispense the cash.
3) I don't think many UK card issuers use multiple applications for the same context. That is to say, if you put your card into an ATM, only one application is likely to be compatible with that profile. There may be other applications for travel (ITSO, for example, is a travel card standard built on Global Platform). I think every EMV terminal has support for application selection menus (usually in the form of little buttons along the side of the screen) but they're virtually never used in the UK.
In my experience while travelling, US payment terminals are the most unusual.
You've then got to request a replacement card from your issuer but it does limit the chance of a stranger coming along and retrieving the forgotten card and attempting to use it (for a signature fall-back transaction after damaging the chip, or for a cardholder not present - CNP - transaction).
Bank-operated ATMs will also often retain the card if it's been reported lost or stolen, but this does rob the lucky/brave checkout operator of their £50 bonus if they happen to retain a stolen card that's been used in store.
2. Machines in Europe has been doing this for a long time and it's never been an issue. I guess in the rare case power goes out (aren't these machines on UPS?) it you just call the provider hotline, cancel that card and get a new one in the mail the day after.
3. I have never seen this but i agree this is an issue. That is a unnecessary UX roadblock.