MultiBit Classic doesn't use recovery mnemonic's (aka wallet words)... the only "backup" option for MultiBit classic was exporting your private keys. Refer here:
https://www.youtube.com/watch?v=LaijbTcxsv8Exactly how many words do you have in your recovery phrase? If it is 18, it is most likely a BIP39 mnemonic and should be able to work with Electrum (you just need to click "Options" on the seed input window, and select "BIP39 seed")... if it is 17, it might actually be an old legacy blockchain.info recovery phrase.
No, it doesn't have to be Electrum... Electrum is just the easiest for MultiBit HD as it allows you to specify the Derivation Path. The only other wallets I know of that use the same derivation path as MBHD are both mobile wallets ("Breadwallet" iOS/Android and "Simple Bitcoin Wallet" Android only). For MultiBit Classic, as you have the private keys, you should be able to import or sweep into almost any wallet you want.
If you have the transactionID, you can put it into any block explorer (like
www.blockchain.info) and it will show you the transaction details.