Finally

As a rule, smaller goldfish shouldn't be housed with bigger ones for the reasons you've already mentioned. You might want to consider separating them until the little ones get much bigger. You'll need a 40g tank for that.

The small fish look like fantails, so it should be okay when they are all the same size. Make sure you *know* what kind of goldfish you are putting together. Comets can be aggressive with slower fish and have been known to kill Very Fancy (celetrials/bubble eyes/lionheads)/Fancy goldfish (moors/Ryukins/Fantails/Red Caps). Fancy goldfish are aggressive to slower Very Fancy goldfish.

I can't really tell how big your puti is. How big is that tank? It looks awfully small for three goldfish and anything less than 50g *is* too small.

You'll need to replace the filter ASAP if it is not working or plan on changing the water every day. Goldfish produce a LOT of waste. I am unsure of what that filter is, but it doesn't look capable of double filtering that tank.

Roan

2) That isn't a fan, it looks like a surface skimmer of some sort. Anyhow, there is water coming out of the filter outlet, so its working. The setup instructions should tell you what water level the skimmer needs to operate.