Be aware that 'free range' and ('organic', FWIW) are close to meaningless in terms of animal welfare. Both give a set of definitions for what meets the label, which is then achieved by farmers by the most cost-effective means possible.

E.g. 1 - 'free range' chickens have almost no extra space per chicken compared to battery-farmed chickens, and many die after being trampled by the others. They are at least a breed which can stand on its own legs - battery chickens can't even walk.

E.g. 2 - 'organic' animals must not be fed antibiotics (which means their general conditions must be good enough for not too many to die from disease, which is otherwise avoided by routine antibiotics in feed). This means sick animals are generally left to die rather than be treated, since allowing antibiotics would lose organic status.

E.g. 3 - For eggs: no matter how good the conditions are for the hens, egg-laying chickens are a different breed to chickens-for-meat. Ergo, all male layer chicks are redundant, and are killed immediately on hatching (normal method is to grind the chicks en masse).

Eating animals is not a pleasant thing. Definitely worth reading up on.

(FTR: I eat animals, eggs, and dairy. I'm struggling to find out how to do so ethically, given the current 'ethical' labels are so close to meaningless.)

Re: your 2nd example, that's generally not true. Sick animals are usually given treatment including antibiotics. If the treatment disqualifies them from organic status they're moved into a different food stream. This is done for economic reasons, not care for the animal's welfare. Despite the image of a quaint family farm, most organic food is still a product of large industrial operations; someone like Tyson foods prices chicken similar to airline seats

I find it hard to believe a single chicken, out of thousands, could receive individual attention at all (after they are sexed[0]). I could be wrong though.

[0] https://en.m.wikipedia.org/wiki/Chick_sexing

I think that depends on the country you're in - AFAIK the UK has quite good standards for products bearing the "free-range" or "organic" labels. The UK has also seen a wholesale consumer rejection of battery farming and a lot of shops now stock free-range eggs and meat by default.

I know this is obvious, but just want to point out that all of the above depends on the legal environment of the country the animals are raised in

You should be looking for eggs marked with the keyword "pastured", which is what you actually envision would be expressed by the deceptive "free-range". Pastured eggs are quite a bit more expensive of course.