I am a citizen of Kazakhstan and I have recently travelled from London Heathrow 5 to Dusseldorf, then to Moscow Domodedovo and then to Ust-Kamenogorsk(Kazakhstan). The route from LHR to DUS was operated by British Airways and DUS-DME-UKK was operated by S7 Airlines (date of travel: 20th of December). I have purchased these flights at S7 Airlines website as a single ticket and S7 and BA have a check-in until final destination because they are in Oneworld Group (e.g. it was like this when I travelled LHR-DME-UKK). To mention, I don't have a Schengen visa and hence I am not able to leave transit zone in Europe.
However, at London Heathrow British Airways representative could not check me in until final destination. They have made checks and said to me that I would be able to collect my luggage and check in by myself at Dusseldorf Airport, so my luggage was checked in to Dusseldorf. However, at Dusseldorf airport, Customs asked me for my luggage tag number and said that they will check in my luggage for the flight to Moscow Domodedovo and I was transferred to the terminal of my next flight. At Moscow, I spoke to representative of S7 and they told me there were no luggage for me and I continued my travel to Ust-Kamenogorsk. At Ust-Kamenogorsk airport, I have reported lost luggage to S7 representative and at home I made a report on British Airways website.
On 22 of December, I was called by airport staff and they said my luggage was delivered. When I came to the airport, they brought a bag in the name of a completely different person and it was not my luggage, but it was in a packaging and my name surname was on it. So, I have reported both to S7 and British Airways that it was not my bag and they are currently searching for it.
Do I have the rights to ask for fee compensation from S7 due to inability of full luggage check in?
And: Is there a way for me to speed up BA and S7 to search for my bag and what to do to certainly get a compensation if my bag is gone missing after 21 days?
I understand I could simply not to travel and purchase a new ticket, but British Airways said to me after 20 minutes of checks that I would be able to collect my luggage and I did not expect my luggage to be lost.