How do I load wallet.dat on new PC and import everything into Electrum?
You can also import the wallet.dat directly into Electrum. Bitcoin Core needs to download the whole chain (as you mentioned) so that'll take a while. Without the chain, your transaction are indeed illegal/conflicted. Since you have the wallet, you can just install Electrum and import it there. Electrum doesn't need to download the chain, so your balance would be visible (and accessible, even more important) immediately.