There are 7*6*5*4*3 = 2,520 ways the captain can arrange her schedule.
Yes, the captain can arrange her schedule in any order she wants as long as all 5 activities are scheduled within the 7 days.
If the captain only wants to schedule 3 activities, then there are 7*6*5 = 210 ways to arrange her schedule.
There are 7*6*5*4*3*2*1 = 5,040 ways the captain can arrange her schedule with 10 activities.
Technically, no. However, as the number of activities increases, the number of possible arrangements also increases exponentially, making it more difficult to find a feasible and efficient schedule.