Yes you can add the bleach to the skimmer or slowly around the edge.

Yes you can add too much bleach - you probably do not want more than about 20ppm in your pool with your CYA level - chlorine level is determined by CYA level.

NO - do NOT add algecide - it will cause more problems. Chlorine kills algae. Algecide is only necessary in few instances (like you have a problem over and over again and you have been keeping the proper chlorine levels) and then ONLY as a preventative measure and ONLY 60% polyquat - not the cheap copper-based algecide.

If you keep the right level of chlorine (2ppm-4ppm for your CYA level) you will not have any algae.