1) Depends on how it is framed. A silent choice all by yourself will only change your small impact, but publicly arguing it with others and campaigning to make such a change on a large scale could potentially be more powerful, if still incomplete and somewhat lacking as a full-fledged strategy for animal liberation, in my opinion.
However, here is a tendency to conflate individual ethical behavior with whether the result of that behavior has distinct positive consequences for the animal liberation struggle at large, and when the second proposition cannot be answered resolutely, people also think they have an answer for the first one. But being complicit in the death and suffering of sentient beings, especially when it is in the form of industrial factory farms, is a disgustingly unethical choice if one has the alternative not to, and that is a reason strong enough on its own to opt out. Besides, in reality, the veganism and activism complement each other and offer synergies, especially in the instance of veganarchism, which is one consistent platform for anti-oppression struggles ranging across various different issues.
2) Animal liberation, to me, is the liberation of all animals, including humans, from their roles as oppressed and as oppressors in those cases where that makes sense, as it does for humans for instance. We are all in both those categories to various degrees, because the society we live in is built upon the exploitation of others in many regards.
We wouldn't expect small children, disabled people and other marginalized groups to deal with their own liberation from oppression, or deem them unworthy of it because they cannot consciously help in the overthrowing of the oppressive system, but that doesn't mean they don't deserve our solidarity. On the contrary, that is where it is needed the most.
As for the chickens themselves, taking their lives for a taste preference is a very obvious case of domination and oppression. Taking some of their eggs less so, but considering the bigger picture it is much easier and efficient to provide healthy vegan diets for everyone, and in that way eliminate any oppressive effects on the chickens altogether. That's the theoretical answer. But that said, there are more pressing matters to focus on in practice for animal liberation activists, like CAFOs and the industry at large, so being consistent theoretically doesn't mean that we in practice, right now, should equally focus on free roaming chickens in someone's backyards and industrial-level exploitation.
2.1) Yes, you can, but doing so while tacitly supporting industrial farming, or even in a less blatant way causing death and suffering to animals for a taste preference, would make it a hypocritical or inconsistent position in my view. I can respect that to some extent, I was myself a vegetarian for a time before I went vegan, and a certain dissonance of beliefs and actions is to be expected at various points, as actions slowly change to conform with ones beliefs. But it seems to me that a lot of people want to eat the cake (literally) and have it, by claiming that they are for animal liberation, while they still consider it is fine to enjoy the taste of animals that spent their lives in miserable conditions and/or died for a mere taste preference.
3) Speciesism is "the assignment of different values, rights, or special consideration to individuals solely on the basis of their species membership". For instance, we have no reason to think that many of the non-human animals we have relations with – either directly as pets or indirectly as food – have a perception of pain that is in any significant way different from ours. In this instance, prioritizing human pain above the exact same pain felt by another species, is speciesist. The basis for most of the systemic and institutionalized speciesism prevalent in today's society lies in exactly such judgment calls. The way we experience and understand suffering and well-being, it is also experienced similarly by these other species. There is no reason to value pain, fear or happiness differently between us. Hard as they might be to measure exactly, it is quite obvious that the evaluations are speciesist today in regards to the non-human animals we exploit for our own benefits. Being vegan and speciesist is of course possible. But claiming that a vegan is speciesist because they value the well-being of, say, a cow higher than the well-being of a plant, presupposes that the experiences and perceptions of the plant can be meaningfully quantified as equivalents of those of animals. There is nothing to my knowledge that suggests this to be true (simple stimuli-response examples don't cut it), and until it does, vegans have a pretty strong claim towards not being speciesist in this sense. Even so, if it would turn out that there is a way to measure and a reason to value the experiences of plants, a vegan diet is more energy efficient and requires less plants than omnivore diets, so would still be consequentially a better proposition.
4) I don't identify as anti-civ, and don't know enough about it to say something meaningful in all honesty, so I'll let others answer this.