You either want to add bleach to the skimmer as Ben suggested or in front of a return jet. The idea is to get the bleach dispersed quickly into the water. Either way, pour slowly.

Polyquat 60% algaecide is the only one we recommend using. You may have to get that at a pool store and also the DE powder although I think maybe Home Depot may have DE. Not certain about that, though.

In regards to pumps --- this is a case where bigger is not always better. A pump that is too big for your filter will damage the filter and will blow water through it so fast that it will not do a good job filtering. Before you buy something, run it past our pump gurus here to make sure you have a pump and filter that are sized properly.

Glad things are looking better.