With respect to the mat placement being off centre, the mat can be realigned on the centre line of the rink after the start of an end if players realise it is off centre.
Law 19.2 After the start of play in any end, the mat should not be moved from its original position except in the following circumstances.
19.2.3 If the mat is off the centre line, it should be moved to that line.
With respect to the bowls that have come to rest on the neighbouring rink, outside the rink of play. Those bowls are dead and should be removed from the rink.
Law 27.1 A bowl is dead if:
27.1.4 it passes completely outside the boundaries of the rink of play after being moved as a result of play; or
27.1.5 in its original course, it passes outside a side boundary of the rink on a bias which would prevent it from re-entering the rink of play; or
27.1.6 in its original course, it comes to rest outside a side boundary of the rink, even though it may have come into contact with the outside edge of the jack.
In the above situation the eventual decision on what to do should rely on the provisions of the Laws of the Sport and also on the common sense and spirit of fair play. Perhaps to declare the end dead and replay it should be the ultimate solution, even though the Laws do provide a precise solution to the situation it may not be the fairest one.