How much oil is necessary to fry/cook eggs?
Technically, an egg is not &quot;fried&quot; unless there is at least some oil involved.  So even though you could cook an egg in a very well-seasoned cast iron pan with no oil, it wouldn't technically be a fried egg.
The primary reason you use oil, though, is to keep the eggs from sticking.  So in a pan like yours -- a worn-out nonstick pan that's not really nonstick -- you're going to need oil, and probably a fair amount.
The exact amount is going to vary according to three factors:

How large your pan is
How many eggs you are making
How &quot;sticky&quot; the pan is

So if that nonstick pan is only 6&quot;/15cm, just a tiny bit scratched, and you're making two eggs, you can use just 2 tsp of oil.  But if you're cooking 8-10 eggs in a 14&quot;/35cm nonstick pan that's completely scratched up, then you'd need more like 4oz/100ml of oil.
Which brings us to the other reason to use oil: flavor and texture. Some ways of making fried eggs use even more oil.  For example, the standard Thai fried egg is cooked in a pool of oil 1/2&quot;/1cm deep or more, in order to get lacy, crispy whites.