Etherium derivation path question

I'm going to generate my HD wallet on an offline raspberry Pi. I'm a little confused on the derivation paths.

Specifically, https://iancoleman.io/bip39/ will generate valid ETH addresses in some cases, but not others.

Valid:

m/0 for eth:

0x9D4C68703fA6638B6B5f061999F7c5bD3f58F64e

m/44'/60'/0'/0:

0xaFeC42a19b08483e641d245960a80879620Ae966

Invalid:

m/49'/60'/0'/0:

3E5TKWX434EQQAkqEFhvAFirjCWGARB8Sg

m/84'/60'/0'/0:

bc1qfn22xjd66jzdty78nggzlrwtrxyckfmu7lvgam

Is the site missing something for ETH in the second two, or is there just no valid ETH address for those standards?

If I use the same mnemonic phrase and the same "purpose" for all my coins, does that mean I'm stuck with bip-44 for my btc and others?

Wikipedia said the address needs to start 0x and is a specific hash of the public key. Would I be able to do that to turn the invalid addresses Into valid ones, or will that result in a random address that my private key doesn't access?