Different between v2Router and v3Router, and which is best

Dear fellow developer,

I would like to inquire about the differences between Uniswap V2 and V3 Router and which is currently the best option. Additionally, I am experiencing an issue where the liquidity I have added to my token on Uniswap is not showing on other DEXs, such as ShushiSwap, where I am receiving an error message stating "no trade found." Is it normal for liquidity added on Uniswap to not be reflected on other DEXs?

Furthermore, I accidentally deployed my smart contract to the wrong Uniswap router address and am unable to withdraw my liquidity. Is there a way to resolve this issue and withdraw my liquidity? Finally, I would also like to know the correct address for the Uniswap V3 Router.

Thank you for your assistance.

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