How do mining pools connect to the Bitcoin network and miners connect to pool?

How do mining pools connect to the Bitcoin network and miners connect to pool?

I couldn't find the answer anywhere so I start a thread.

  1. How do mining pools connect to the Bitcoin network to propagate transactions and blocks? Do they run their own full node? If yes, how many of full nodes? I presume it's hard to run a mining pool with only one full node because it's IP will be exposed to some network attack like DDoS.
  2. How do miners connect to a pool? Is there any server running by mining pools so miners can connect to?
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