Old kitchen range only has 3-wires, how to wire correctly to 4 wire circuit
First the easy one:

The range's green wire was connected to ground. This is wrong right?

Actually, that is correct!
Now on with the show:
The usual correct wiring for a range is:

2 x hot = typically black &amp; red
1 neutral = white
1 ground = green or bare (or metal conduit)

In addition, the wires must be properly sized based on the current used by the range (big enough), and the breaker must be sized accordingly (small enough). For example, a 30A circuit will require at least 10 AWG wire (8 AWG is fine, 12 AWG is not) and a 30A breaker (smaller will result in nuisance trips, larger will not protect the wires from overheating).
You need to figure out what size wires and what size breaker you currently have. You may need to upsize one or (more likely) both to properly support the new range.  Need to check with specifications of the new range.
There are certain situations - and you have at least one of these - where you only need 3 wires:

If the range only uses 240V and does not make use of 120V power at all, then it does not need or use a neutral, or have any connection for a neutral wire. That appears to be the case here. Most, but not all, newer ranges use 120V to power clock, timer, controls, etc.

If the range was installed a long time ago on a circuit that was installed a very long time ago, then a separate ground wire was not originally needed and ground and neutral combined was permitted at the time and is a grandfathered exception. In some places it is still a grandfathered exception. However, if upgrades to the wiring are needed (e.g., to change from 10 AWG to 8 AWG wire) then the exception goes away. This is not the case here, as you already have a 4-wire supply!


As far as the burn marks, etc. Those are serious problems. They could be due to undersized wires, but more likely due to loose connections. A loose connection can lead to arcing and burning and/or be high resistance which leads to overheating and burning. So cleaning up those connections is critical. I am extra concerned about the burning on the white (neutral) wire, which since it was not even connected should never overheat! Which indicates that there was likely some serious arcing going on that it burned the otherwise inert wire.
As noted, the range whip installation is not correct, and clearly there were other problems as well. Cleaning all of that up will help for now, but it may need to be all redone for the new range with new wires. I would certainly be concerned about the damage to that white wire since it will likely be needed for the new range.
You need to figure out what kind of wires you have (cable or individual wires, what size), what breaker you have, and what breaker/wire will be needed for the new range in order to decide exactly how to proceed with replacement.

Based on comments, updates, etc. This appears to be 8 AWG on a 50A double-breaker. Typically 8 AWG wire should have a 40A (or smaller) breaker. There are plenty of options that should work fine with that. I picked a GE 30&quot; slide-in range with 4 burners and a self-cleaning oven at random from Home Depot, and the manual shows 240V @ 40A. So there is a good chance that if you swap the 50A breaker for a 40A breaker and clean up the wiring that you will be able to use this for a new range.