I am fairly young, not a teenager yet. This morning, my parents had a fight and my mom said she was going to stop cooking for my dad. At lunch, I spoke to my dad about apologizing and recognizing my mom's importance in the family, but he ended up making lunch for himself. I am scared my mom would start taking more and more things away until they reach the breaking point. Is there anything I can do to prevent this from happening??
Ultimately, responsibility for solving your parents' relationship problems lies with your parents.
There are things you can do to encourage your parents to work out their differences. But the fate of their relationship is in their hands, and if they are unwilling to work to solve it then there is very little you can do to force them to.
The best thing you can do is to try an understand the point of view of both your parents, so you can help each of them understand the other. And just your presence gives your parents an incentive to work out their difficulties.
Your father making himself lunch isn't necessarily a bad sign
You can see a breaking point for your family where your mother refused to do an increasing number of chores until it is too many. But there's a second breaking point, where your mother is handling too many of the chores herself and can no longer deal with the weight.
I do not know what the equitable division of labor is in your family. But for many, many families, women do more than their fair share of the chores. There is a reasonable probability that your father making his own lunch is a sign that your family is moving in a healthier direction, rather than a dangerous one.
Far more worrisome would be if your father refused to make himself lunch, starving himself to guilt trip your mother, or even ordering out. Making his own lunch might be a sign that he has acknowledged your mother's point.
Take a look at the work that goes into making your family household work. This is a hard thing to do, and there are many little things that are easy to miss. Cooking, cleaning, and making money are obvious, but "scheduling doctors appointments", "making sure the kids are doing their homework", "noticing that the trash needs to be taken out" and things like that can be more subtle, but are still work. There is an emotional cost to some chores that doesn't necessarily line up with the physical labor of the task.
Look for places where you can assume responsibility yourself. Taking out the trash, or making sure you do your homework unprompted. By reducing the number of chores your parents need to handle, you will make it easier for them to find a balance that works between them.