I was a random breeder too, and got all 7.

For #2 I did use some strategy. There is a cheat sheet somewhere out on the internet that shows what all 7 fish look like ( I did a google search). Based on what #2 looked like, I was able to get it. But it still took me a while even though I saw the end result.

Someone has posted another kind of cheat sheet that will show you what happens when you breed certain fish together.
You can scan the message board for that.