mobile

I've seen countless of threads about this but none gave me the answer.
What I have:
stock*** recovery
adb
a firmware for my model, a zip with a file called update.img
odin
What I don't have:
any custom rom for my model
any custom recovery for my model
adb shell, my system files being corrupted
download mode; tryed countless times to enter it by adb, by power both power buttons holded plugging usb than just pressing the up button; by holding just the down button, everytime it booted into recovery but not download

Any advise how can I flash that firmware? I think I might need some next-gen tool.
Or if I can't flash that firmware, any advise how can I replace system so I wont any errors in ADB?
Im out of warranty.