Can't answer the first two but tidying the strawberries depends to some extent on what you want to do with the runners. If you don't want to grow new plants from them just cut them off and keep the area weeded. If you have room its a good idea to start off some new plants though. You can extend the bed with them if you have room or even grow them in pots. That way you will always have some vigorous new plants to replace older ones.

Thanks Stera , it is years since I had a go at the patch properly .