A grid tie inverter is tied to the grid so that it can track it's voltage, no grid voltage = no output as there is no line voltage to track, even your £50 crap from china does that as it's fundamental principle of operation of a grid tie inverter.
Yes, but there are also "grid interactive" inverters which tie to the grid but also work as off-grid inverters running off of batteries when the grid goes down.
There are also
"AC coupled" inverters (see
here for more detail) which are able to supply AC power direct from standard grid tie only inverters - even in a grid outage - by coupling into a battery based system.
In addition, I believe SMA has a product out now that allows you to tap directly into some of your grid-tie only PV production during a power outage - without batteries.
In the USA all grid tie or grid interactive inverters are required to meet
UL 1741 anti-islanding requirements to ensure safety of utility workers.