I don't do solar, but I will try and answer your questions as best I can
First off phase imbalance, the three-phase supply from the sub-station to your street (or local area covered by that supply) is normally split into groups of houses fed from each phase to balance the load out from the suppliers, this is done in various ways, it could be that 3 houses are fed with L1 and N, then the next 3 with L2 and N the next 3 with L3 and N... and so on, or in some other arbitrary way, but they will be evenly spread out so each group of houses gets a single phase + Neutral supply but on different phases to load balance.
The Inverters which convert the DC from the panels on the roof to AC will amongst other things such as regulate the voltage and synchronise their supply with your incoming mains (it needs an incoming mains supply to synchronise to) will trip out if there is a loss of mains supply, this is so you cannot backfeed on to an otherwise dead supply network (this is very strictly enforced).
This is mainly so that an unfortunate linesman who maybe knee deep in water down a hole in the road doesn't get a belt whilst trying to repair the cable, or other users/operatives of the network, also your inverter (typical domestic feed in tariff types) would not have the power to maintain a supply to all those other houses on the same phase as you (see above) which will have their own loads still connected.
As far as I am aware the inverters (typical domestic feed in types) do not auto-start on re-application of mains, they used to have to be manually re-set, Rob (glowing anode) has had more to do with PV than I, so he may clarify this latter point, although some large commercial or industrial ones may well do, as these types typically have much more sophisticated controls and monitoring equipment by their very nature.
There is another form of Solar power that works in a similar way, only it does not feed into the public supply, this stand alone system is called islanding, this is typically used to power sheds or boats etc. and may use the DC to charge batteries or even to power say Dc lighting directly, it may also use a different type of inverter to power stuff locally, but it will not connect back into the grid.
I have greatly simplified this, as some systems are highly specialised and some can be a sort of hybrid, also some I am not that familiar with