Upvote:3
Do I need a visa to Spain (transit or short stay) to board my plane from the UK?
Most likely yes. Vueling sold you a flight to Spain and they are required to check your eligibility to enter the destination. What happens when you get there is not their concern. If you are lucky there are regulations that exempt you if you stay less than 24 hours and have proof of onward travel. Put your details in https://www.iatatravelcentre.com/passport-visa-health-travel-document-requirements.htm and see what you get. You would also need to call Vueling and confirm that they accept your booking.
Can I stay in the international transit Area even though the flights are not connected?
Unlikely. This depends on the layout of the airport, your specific flight details and the current check-in procedures. For the layout related stuff, check https://www.aeropuertobarcelona-elprat.com/ingl/flight-connections-barcelona.htm
You will need a boarding pass and you apparently can't get for Air Algerie airside in Terminal 1. So you would have to check in online. Unfortunately check-in procedures during Corona are unpredictable and change frequently. Many international flights don't allow online check-in since the airline has to do a manual documentation check at the check-in counter (passport, visa, corona test, entry forms, vaccination certificates, etc.)
Can I get my checked luggage in the transit area to check-in again for my next flight?
No
Or should I just take hand luggage
That would help.
Relying on an airside transfer is very risky and by far the safest route is to plan for full legal entry into Spain and allow at least 4 hours between flight.