Eating a wild animal that died on it's own would be vegan yes but I'll give you a heads up that questions like that don't tend to go down pretty well with vegans cuz it comes across as a gotcha and they get that a lot. Like is the practical implication there that there are people that would go vegan if only they could eat roadkill? I'm sure you don't intend it to come across that way but I thought I'd let you know.

As for eggs, while keeping your own chickens is better than battery farming it's still problematic. Hens don't naturally produce the insane number of eggs that we're used to. A wild chicken will generally produce 12-20 eggs a year similar to how a woman has a period but when a hen's eggs are taken away from them they instinctively produce more leading to the hundreds per year that battery hens lay. Laying eggs uses a lot of calcium for the shell so forcing them to lay way more than they're naturally used to is very bad for them. Normally a chicken will eat it's own eggs to replenish the nutrients lost during laying so by taking the eggs of your backyard chicken you're forcing it lay more eggs than it should and denying it the nutrients to sustain itself.

Your point about stopping egg production entirely is on the assumption that we're able to stop it overnight which no vegan is naive enough to think. The veganisation of society is something that will happen gradually over many years so there is no worry of some overnight chicken re-wilding that must happen.

As for the last point there are wild chickens in the world atm and it's very unlikely to be the case that battery chickens will all be released into the wild they will just be bred less and less for exploitation.