How to verify, with different airlines, that the broker booked the flight correctly?

I bought 3 interconnected flights via Kiwi.com, but have been reading so many negative reviews and experiences with this online broker. Many of the problems look to be connected to the booking not forwarded to the airlines, or details (e.g. regarding additional luggages) not transmitted (leading to pay again when checking in at the airports).

I wonder what I can do to prevent issues when I will travel to such flights?

• Is there a way to have a confirmation of the booking (with my name and passport number) from the airlines, so that I can be sure that my flights have been requested and paid?
• Checking the state of flights on some flight-tracking website, so to be aware of eventual variations/cancellations/delay.
• I've also paid for the Premium Insurance but I'm not sure if that would help.
• Would it be better to try to get a refund and buy with via another company?

EDIT

From the confirmation email I have:

• a PNR (same for all 3 flights)
• 3 E-Ticket numbers 1 single E-Ticket number

PNR is in the format accepted by the first airline, but is not recognised by the system on the website.

The second & third flights airline (Etihad Airlines) website says

No special characters or numbers allowed

regardless of what I digit. I tried their Check-in form, that doesn't give the error but says my booking doesn't exist...

Additionally CheckMyTrip reports a different PNR for the 2 Etihad flights (but still not recognised on their website), not appearing at all in the ticket sent me by Kiwi.com...

What can I do?

EDIT 2

I called all the different airlines to confirm the booking of the flights, the inclusion of the luggage and the eventuality of automatic pass-through for the luggage at the changing airports.

Also, Kiwi.com specifies for each flight that the passenger will have to check-out and check-in again (having to pass again all the security controls, and actually eventually having a visas to just step-in & step-out of the country). Calling the single airlines confirmed in which cases the pass-through is automatic (for example with Etihad I won't need to do anything, regardless of what the default text from the Kiwi.com confirmation says).

To note that the for almost all airlines customer services I got the chance to call in my country to speak in my mother language and confirm all the flights. Also the PNR given by Kiwi.com was not valid for any of the airlines, but they gave me the right PNR after providing the ticket number.

I can only suggest to spend the time (and hopefully not the money) to call and verify each step of your flight with your airlines. Usually their customer services are a lot better than the customer services from online brokers (e.g. calling eDreams they gave me 2 other different numbers to call to get minimal info about the flight: 1 for free, fake; 1 highly expensive, working).

EDIT 3 - All right!

I finally got my flights. Everything went smooth. I confirmed before leaving (twice, in two different airports) that the passage of luggage is automatic when there is a single ticket number. What Kiwi.com writes in its email is just misleading; probably an automatic text just to disclaim any responsibility in case something goes wrong.

Not really professional.....

I'd suggest to use Kiwi.com just to find routes, not to book. Or to book with them just when having already some experience and confidence with international/intercontinental travelling (to not get confused by a fuzzy booking agent).