When you have an algae bloom sometimes that is referred to as "green water", like Andrea said.
This is a good sign that your tank is healthy. Algae is not all bad, here are some good things about algae!
Fish eat it and it is good for their digestion, algae will absorb nitrates in the tank.
It is unsightly but you can use a scraper, algae magnet, or soft pad made for aquariums and wipe the front of the glass so you can at least see your fish!
As far as eggs, they are tiny! They are about the size of pin heads, clear white in color. A female goldfish will lay these eggs but you will have to have a male goldfish in the tank to fertilize them for them to hatch and babies to appear.