This page holds answers to important questions of general interest asked by students and some clarifications about the homework assignments.
There is not a fixed number. I recommend you to choose start states that are good for comparison of various algorithms and heuristics.
For example, it is possible that one student has 10 random start states. But they might be very similar to each other and might not reveal the differences between various algorithms and heuristics. Another student might have just 5 random start states. But they might be very insightful. The latter case is preferred. That is why there is no fixed number I can recommend.
To summarize, you should prefer to put in the report start states that represent the strengths and weaknesses of various algorithms and heuristics.
The time-complexity of finding the number of minimum hops will be high. That is why, it is not practical to use this information. And we cannot accept this information as given as the straight-line distance, since it is part of the solution. Generally, if you need to do exhaustive search to compute a heuristic function before running the heuristic search, then you shouldn't use that heuristic function.
For the route finding problem, it is somewhat difficult to come up with interesting heuristics. Don't worry too much about finding a perfect heuristic function for that problem. Focus more on the heuristic for the 8-puzzle.
You should use Python 2.x instead of Python 3.x.