I don't remember GM that much since I switched to mac, but
To make the moving object, you could either
1. Make it move in a random direction and just have it bounce off the walls
a. make an object thats a wall and put it all around the room
b. Make an event for the object I think theres something like a "bounce off object" event. Just try pressing buttons you'll get something
2. You could make the object move in random spots by making a step event
a. in the step event you could make an event that says move to a random position (theres an event for that)
3. I'm not sure how to make it move away from the mouse
For the timer, you could
1. Make an object
2. Do something like: Make a step event
3. Under the step event, make something like: Every X steps add 1 to score/variable/whatever
4. Then: collision event with the mouse (or upon mouse click) stop adding score
a. I'm not that great at gm so I would usually destroy the object so the score stops going up.
Hope that helps!
Just experiment! Keep on trying to do different things!
Sorry if thats confusing...