Confusion about rollups

I grasp Layer 1 fine now (finally lol) with all the things smart contracts can do and stuff. The arrival of Layer 2 rollups is getting me some confusion I'd like to resolve. Like I grasp the high level concept of moving the computation offchain and using L1 data availability for proof batches and what not, but I still have some confusion on more specific aspects:

• From what I gather, projects on L1 have to be launched again on all the rollups individually. e.g. Uniswap launching on Optimism, then Arbitrum, and probably zkSync at some point. Does that mean the Uniswap on Arbitrum exists independently of the Uniswap on Optimism? As in, separate liquidy pools on each one and stuff?

• At some point we'll probably see projects launching exclusively on Optimism (at least at first). So if that project has an ERC20 token, that token will only exist on Optimism, correct? Meaning there's no possible way to bridge it to mainnet or Arbitrum/zkSync? Or am I missing something like the ERC20 smart contract has to exist on mainnet first for the transactions on Optimism to be valid?

• Pretty much same as above, except with NFTs. If you mint an NFT on Optimism can you bridge it anywhere else?

• Is it gonna be as simple as switch Metamask from mainnet to Polygon? Or is there a more involved procedure to do transactions on L2 projects?