I am looking for advice, ideally step-by-step, on how to "recover" or "move" the BTC inside the Guarda multi-sig wallet, to another different wallet, as we have absolutely no idea what to do or where to start
I'd say start with Electrum. See if you can recover your multisig wallet there.Quote
Again, our aim is literally just to get the crypto out of the Guarda Wallet onto another one (not sure which) using the private keys
Step 1 would be to decide which secure new wallet you're going to use. You'll need to know where to send your Bitcoins.Quote
We both have access to the "private key" of the wallet.
Is it a private key, or a seed phrase?Quote
1. If I am able to recover the BTC with just MY private key to the wallet, does that not defeat the purpose of the multi-signature system? As that would mean I can just import my private key and recover our shared BTC from my co-signer just by myself?
A 2 of 2 multisig wallet requires signatures from 2 private keys.Quote
2. I may have understood incorrectly, but would me and my friend have the same private key as it's a multi-signature wallet, or would they be different? And if they are different, how would we actually recover the crypto from our Guarda Wallet and put it onto another wallet?
The keys should be different. Basically, one of you creates and signs a new transaction to transfer the Bitcoins, after which the other person has to verify and sign the transaction to make it valid. After that, it can be broadcasted.Quote
There's been a bug since December; where if you broadcast a transaction, the co-signer cannot see it, hence cannot sign/broadcast it, leaving your crypto in limbo.
Can you manually export the transaction and email it to the co-signer, so he can import and sign it? Again, I don't know "Guarda", but this sounds like the easiest solution. 
