Why does she tear it down in the winter? Avoiding chemicals, especially the bad ones, is preferred. The fact that birds were dying must mean they were not safe chemicals. There are safe things you can use to control algae - good bacteria, barley straw (or pellets or extracts), UV sterilizers, better filtration, plants, more plants, etc. If you have to use an algaecide, AlgaeFix is the safest one I know of. At regular doses, it's only toxic to crustaceans and perhaps some micro-life. My algae page is at
http://www.fishpondinfo.com/algae2.htm"It has two pumps/filters, 50 goldfish, no plants, plenty of sunshine, holds 500-600 gallons of water, and no leaves can fall in, because my dad built a see through shelter around it."
The pond has too many fish (unless they're babies) and no plants. Reduce the number of fish and add plants, and the pond will become much healthier and more clear.
"Is there anything else we can use instead of chemicals to clear the water?"
Yes, see what I said above.
"Could it just be a considence that the birds were dying when we did use them?"
How many birds? Which species? Where did you find them? I very rarely find dead birds so if you found a bunch, poisoning is a likely cause. It may not have been from the pond water for sure, perhaps someone used pesticides, and birds ate the insects carrying them.
"Also can a person leave the pond up with the fish all winter or is what she is currently doing okay?"
Where do you live? Unless you live in a super cold area, you can keep the pond running all year. See
http://www.fishpondinfo.com/winter.htm for information on wintering ponds. My fish all stay out under the ice. As long as there's an opening in the ice, and the pond is well aerated and otherwise healthy, it shouldn't be a problem. You can certainly bring the fish in if you want but there's no reason not to keep the pond full and alive all year even if the fish aren't there.