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I want to travel to Kuala Lumpur from Frankfurt with Turkish Airlines, with a stop in Istanbul for 2 hours. Since I have 2 different tickets with different booking numbers, should I take my checked baggage and re-check-in again? And do I need a transit visa for that?

Edited in from an answer (about to be deleted now)

I have to deal with this problem. I just bought the tickets from skyscanner, and realizing that they have two different booking numbers after I paid. I have tried to cross-check to the airlines regarding my case, and they told me I do not need a visa (but I am not sure: than I went go www.turkeyvisagov.com and I didn't find Indonesia required visa in Turkey, please correct me if I am wrong) ,

I also went to www.turkishairlines.com, for finding information about my baggage, they stated that for transfer passanger (who have stopover of less tha 24 hours anywhere between the start point and final destination of their journey who boarding a connecting flight with the same or different airline company), when disembarking from the aircraft, take your carry-on baggage and continue directly to the boarding gate. If you do not already have a boarding pass for your flight, obtain one from the transit check-in counter. And the luggage can be taken at the final airport.

I hope it will be true, that I do not have to take my luggage from my first flight, and bring them for check-in for my second flight, and also I do not need a transit visa at all.

This will be a tough connection to make, consider rebooking.

If it's separate tickets, you need to retrieve your luggage after the first flight and check it in IST for the second flight with the second airline.

In most international airports the only way to the baggage claim is through immigration and then out into landside area of the terminal. In this case you would need a visa (try this to determine https://turkey.travisa.com/VisaInstructions.aspx?CitizenshipID=US&CountryID=TR&TravelerTypeID=TR&ResidenceID=US&PartnerID=TA&state=16679 )

Then you need to get to the check in counter, get a the boarding pass for your second flight, drop the bags, go through security and immigration again. Keep in mind that for international flights, bag drop off often closes 45 to 60 minutes before departure.

I'm not familiar with the details in IST but unless there is a way to get from baggage claim back to the airside part of the terminal and the second airline offers airside checkin, you are unlikely to make this connection.

If you miss the connection, you are on your own. The airline will consider this entirely your fault and the airline has no obligation to help or accommodate you in any way. They might, but they also might not, and chances are you will have to spent significant extra money to get to your destination .

I strongly suggest calling the airline of your second flight and asking them about their detailed setup in IST and potentially re-booking to a later time.