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https://feeds.chain.link/ - link for reference.

Let's take the LINK/USD feed for example: From my understanding, the aggregation contract fetches the price of LINK in USD from the node operators who get their price from other aggregation services. Then, smart contracts of other services e.g synthetix fetch the data from this contract and use the price? Does it take the volume into account? Is this the VWAP? Or is this the TWAP?

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The price feeds / reference contracts work as you described:

  1. Independent Chainlink nodes collect data from highly respected APIs
  2. They place the data on-chain
  3. Other services make calls to the reference contracts

The price given is considered the last price which is what most all exchanges consider to be the "market" price. Most exchanges have some logic to remove outliers, so someone who randomly sells for $0 isn't going to reflect as the last price.

VWAP is the volume weighted average over a specific period of time, this wouldn't make sense since we are looking for the most recent price.

TWAP makes even less sense, since this is the time weighted average, without regard to volume.

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