I think your co-worker definitely needs to think more about what she’s saying. What she said about your eating habits in front of the boss wasn’t cool because 1) it challenged your polite excuse for not going to lunch, which is rude, and 2) it implies you think more about food than work and stick to a rigid routine. So yeah, either pretty dumb on her part or she’s trying to make you look bad. And asking someone how old they are at work unless among friends, also not really cool. Age shouldn’t really be considered in the workplace. It can perpetuate biases and so on. It should be about tenure, years of experience, and above all skill and talent and competency. My boss is always asking how old we are and I hate it.
But what she’s done in these two instances doesn’t really rise to the level of bullying or harassment. I would talk to her when she says these things. If she asks how old you are, “why do you ask?” If she pushes, “old enough to be out on my own.” And maybe “hey, the boss doesn’t need to hear about my eating habits, okay?” After the fact. In the moment you didn’t need to get defensive, you could just kind of look at her blankly and say “yes we usually do eat around noon.” Or, “…and?” Because wtf. That’s totally normal!
What I’m saying is call her out and shut her down and then move on. You can’t really give a co-worker the silent treatment. You can choose to have less engagement of a personal nature though.