I think that perhaps the biggest point here is that chemically identical but ethically "clean" dairy products could be developed using humane methods, and this would allow consumption with no ethical ramifications. However, that isn't immediately viable or what you're asking, so I've attempted to address your sub-points more closely.
a) To borrow from economics, animals could reasonably be held to own everything they produce themselves. I believe that technology is the long term solution to no intervention: eventually we put all the humans in spaceship and fly off, leaving Earth as a nature reserve (maybe clean it up a bit first). The costs of doing this immediately would be incredibly high, even just measuring in terms of animal welfare, but in the mean time I believe equal consideration is a fairly reasonable guide as a global utilitarianism (across species). As plants don't implement nervous systems, they can be reasonably held to either have no utility curve, or at the very least, the worst possible endocrine distress a plant can experience can be held to be less costly than that of any organism with a nervous system. I would argue that equal consideration does hold for plants, it's just that they experience pain and utility to a lesser extent due to their structure's natural tendency toward stoicism.
b) Reproduction and associated overhead are not zero cost processes, that is, even if there is sufficient milk for offspring, a maternal mammal would still have to more rapidly deplete her body to provide additional milk. As this is nonconsensual by definition, it is relatively difficult (but not impossible) to defend morally.
It is important to consider that this probabilistically increased milk production and associated body degradation is a low cost operation, and violation of rights in this case may be globally optimal in equal consideration as, for example, the provision of milk for a human caretaker may be considered a form of mutual welfare or a service purchased with labor. In some cases, the greater good invalidates the need for consent. Just as paramedics are permitted to assist unconscious patients incapable of communication, it is not unreasonable to argue that a non-consensual partnership between humans and other animals is not just ethically acceptable, but possibly necessary. Perhaps a better example is the idea of spaying and neutering cats and dogs- non-consensual, a violation of individual liberties, but generally considered a moral mandate.
As mentioned earlier, eggs are an even more difficult argument, but it could still be made.