I always leave trades open over the weekends. Maybe if there were really big news expected (something like Grexit or Brexit) I would stop the strategy but otherwise I think it unnecessarily decreases the profits. But it depends on the money management too...

That said - if the strategy becomes unprofitable when closing the trades over the weekends I would double check it if it really has enough edge.

Some strategies can be run without any optimalization. Sometimes, the optimalization can even decrease the robustness of the strategy. But when you optimize I think you have to decide for yourself what's the best retrain period for the particular strategy. You can run some experiments to determine that.