To answer your listed questions:
- It will depend on whether kiwi booked the actual flights unter a single PNR. It is not neccessarily the case that they will, even with airlines with interline agreements, they can still buy different tickets under different PNRs for you, as this may or may not make the whole booking cheaper. You will have to wait for the answer by Turkish to get clear facts here, or you can look through all documents provided by kiwi to see if there are different PNRs in there (e-ticket, receipt, ...). AFAIR, the kiwi booking as a whole may also have another PNR, if they booked single flights with different PNRs.
- That means for kiwi.com, that they will not check you in automatically and you have to do it yourself with the airline - Turkish will in fact provide a boarding pass, but you have to request it yourself using your PNR, subject to Turkish's policy.
For us to be able to answer your actual question, whether you'll be able to actually travel with this booking, we need more information as others have stated in the comments:
- Your citizenship
- Your complete itinerary
ADD → IST → GRU with Turkish airlines and GRU → BELEM → PBM with GoL Airlines
- Were all your flights booked on a single PNR by kiwi?
- Does your booking say "connection protected by kiwi/the airline(s)"?
Probably doesn't help you with the exact question, but it is a good read anyway in case of problems along the way: Q: What does the “Kiwi.com Guarantee” cover?
You will probably need a visa.
Since your booking is split over your flights, it can be argued that it TWOV does not apply to you. You do have all the flights on one e-ticket, but I don't know if that's sufficient. But what's worse, your flight GRU - Belem is a Brazil domestic flight. It is very likely that TWOV doesn't apply to domestic connections at all. This might also mean that a "airport transit visa" - if such exists in Brazil - isn't sufficient either and you have to get a full visitor visa; this would be the case in Germany for example.
Brazil - Transit Visa
Transiting without a visa is possible for:
Passengers with a connecting flight booked on the same ticket in transit.
This TWOV facility does not apply at Curitiba (CWB), Florianopolis (FLN), Porto Alegre (POA), Porto Seguro (BPS) or Salvador (SSA).