Ethers.js: Can You Get the Transaction Hash from a PairCreated Event?

You don't sign a request with a signature, you sign a transaction. You cannot generate generic signatures to be associated to transactions later on, you need to have access the complete object you want to sign - the raw transaction in your case - before the process works correctly.

Each library and wallet has its own signing implementation. With ethers.js in particular, you can use the Signer object to sign a transaction. From the [ethers.js official documentation][1]:

signer.signTransaction( transactionRequest ) ⇒ Promise< string< DataHexString > >

Returns a Promise which resolves to the signed transaction of the transactionRequest. This method does not populate any missing fields.

Sub-classes must implement this, however they may throw if signing a transaction is not supported, which is common for security reasons in many clients.

Signer usually refers to an external wallet - i.e MetaMask - not controlled by your ÐApp.

If instead you control the wallet with your app - so not a ÐApp anymore ;) - below some examples of signing transactions and messages with ethers.js and a wallet. You can find them inside the [Wallet official documentation][2] also:

    // Create a wallet instance from a mnemonic...
    mnemonic = "announce room limb pattern dry unit scale effort smooth jazz weasel alcohol"
    walletMnemonic = Wallet.fromMnemonic(mnemonic)
    
    // ...or from a private key
    walletPrivateKey = new Wallet(walletMnemonic.privateKey)
    
    walletMnemonic.address === walletPrivateKey.address
    // true
    
    // The address as a Promise per the Signer API
    walletMnemonic.getAddress()
    // { Promise: '0x71CB05EE1b1F506fF321Da3dac38f25c0c9ce6E1' }
    
    // A Wallet address is also available synchronously
    walletMnemonic.address
    // '0x71CB05EE1b1F506fF321Da3dac38f25c0c9ce6E1'
    
    // The internal cryptographic components
    walletMnemonic.privateKey
    // '0x1da6847600b0ee25e9ad9a52abbd786dd2502fa4005dd5af9310b7cc7a3b25db'
    walletMnemonic.publicKey
    // '0x04b9e72dfd423bcf95b3801ac93f4392be5ff22143f9980eb78b3a860c4843bfd04829ae61cdba4b3b1978ac5fc64f5cc2f4350e35a108a9c9a92a81200a60cd64'
    
    // The wallet mnemonic
    walletMnemonic.mnemonic
    // {
    //   locale: 'en',
    //   path: 'm/44\'/60\'/0\'/0/0',
    //   phrase: 'announce room limb pattern dry unit scale effort smooth jazz weasel alcohol'
    // }
    
    // Note: A wallet created with a private key does not
    //       have a mnemonic (the derivation prevents it)
    walletPrivateKey.mnemonic
    // null
    
    // Signing a message
    walletMnemonic.signMessage("Hello World")
    // { Promise: '0x14280e5885a19f60e536de50097e96e3738c7acae4e9e62d67272d794b8127d31c03d9cd59781d4ee31fb4e1b893bd9b020ec67dfa65cfb51e2bdadbb1de26d91c' }
    
    tx = {
      to: "0x8ba1f109551bD432803012645Ac136ddd64DBA72",
      value: utils.parseEther("1.0")
    }
    
    // Signing a transaction
    walletMnemonic.signTransaction(tx)
    // { Promise: '0xf865808080948ba1f109551bd432803012645ac136ddd64dba72880de0b6b3a7640000801ca0918e294306d177ab7bd664f5e141436563854ebe0a3e523b9690b4922bbb52b8a01181612cec9c431c4257a79b8c9f0c980a2c49bb5a0e6ac52949163eeb565dfc' }
    
    // The connect method returns a new instance of the
    // Wallet connected to a provider
    wallet = walletMnemonic.connect(provider)
    
    // Querying the network
    wallet.getBalance();
    // { Promise: { BigNumber: "42" } }
    wallet.getTransactionCount();
    // { Promise: 0 }
    
    // Sending ether
    wallet.sendTransaction(tx)

  [1]: https://docs.ethers.io/v5/api/signer/#Signer-signTransaction
  [2]: https://docs.ethers.io/v5/api/signer/#Wallet--methods

This is a SERIOUSLY painful way to take. The router contract has functions called getAmountsOut and getAmountsIn, use them. Simply pass in the token path&amount inputted or outputted and it will return the amount you would receive if that tx were to happen. It accounts for price impact itself, you don't have to worry about that.