I don't understand what question 1 is asking for.
2. To find a maximum velocity you need to solve
for t and show that you have a maximum at that t.
3. Do they really mean average acceleration or rate of acceleration I wonder? By the mean value theorem, the average rate of acceleration is
(By the way, the time rate of change of acceleration is called a "jerk.")
4. The instantaneous rate of acceleration is da/dt.