Does Detect Magic Detect Scrying?

Yes, the Scrying sensor can be sensed with Detect Magic.

Do golems show up on detect magic?

The detect magic spell senses active magic. It doesn't detect past magic. For example, a golem was animated by magic—as if by a jolt of lightning—but that magic isn't now present. The golem, therefore, doesn't detect as magical, unless other magic is active on it.

Does detect magic let you see invisible creatures?

Detect magic won't locate an invisible creature, you need to be able to see the creature or object. There is a spell specifically designed to find invisible creatures or objects, See Invisible 2nd level.