This depends a bit on the kind of exercises you do.
There is a little debate in the fitness community if exercising in the morning with or without prior breakfast has an effect on fat loss. The theory is that your glycogen levels are low and your body has to burn fat to compensate. However as far as I recall research could not show that this is true.
So back to the exercise, what definitely is true is that your glycogen levels are somewhat lower after sleeping. If your exercise is only a jog around the block for some minutes, this probably does not matter. If it is a full weightlifting routine or a prolonged cardio session (eg running for an hour) you will probably feel exhausted easily without a prior meal.
On the other hand a full stomach might also have negative effects on your workout. Some people (including myself) don't like working out with a full stomach or even get nauseous.
So the decision you have to make here is what you like more; working out with a full or an empty stomach. You could also eat something before and the rest afterwards. Splitting meals has the advantage that you might want to eat less, which can come in handy if you are trying to lose weight.
For the other actions: Go to the toilet when you need to, I would do that as first thing in the morning, as a full bladder doesn't feel good and you gain nothing by holding stuff in. Take the shower after your workouts, unless you want to annoy people.