Can you explain the pensieve and how it works with memories?

Yes, actually this one has been answered by Rowling herself so we don’t have to elaborate much. 

She was asked: “Do the memories stored in a Pensieve reflect reality or the views of the person they belong to?”

Answer: It’s reality. It’s important that I have got that across, because Slughorn gave Dumbledore this pathetic cut-and-paste memory. He didn’t want to give the real thing, and he very obviously patched it up and cobbled it together. So, what you remember is accurate in the Pensieve.

Asked: So there are things in there that you haven’t noticed personally, but you can go and see yourself?

Answer: Yes, and that’s the magic of the Pensieve, that’s what brings it alive. (…) Otherwise it really would just be like a diary, wouldn’t it? Confined to what you remember. But the Pensieve recreates a moment for you, so you could go into your own memory and relive things that you didn’t notice the time. It’s somewhere in your head, which I’m sure it is, in all of our brains. I’m sure if you could access it, things that you don’t know you remember are all in there somewhere.

Pensieve memories are not susceptible to bias, they are a completely accurate rendering of whatever happened regardless of feeling, time, whoever’s point of view it’s from. Nothing taints them unless, as said above, they are manually tampered with and usually it’s fairly obvious when they have been. 

Even if you didn’t see or hear something yourself at the time of the memory (example: Lupin talking about being a werewolf in Snape’s memory. Obviously Snape didn’t actually hear any of their conversation himself but he was close enough to them that it was recorded into his subconscious) you would be able to go back into a memory and examine all the aspects you missed. 

I hope that covered it well enough.