It's so great to hear that you're so eager to start a business at such a young age. I started my first business only a couple of years older than you are now so I'm more than happy to see what I can do to help you out.
Since your under the age of 18 your parents will, in fact, be liable for your store. Basically, your parents would be the store owners until you're old enough to legally take control. Since people under the age of 18 aren't able to sign contracts or get sued there isn't a way for you to be liable while your parent's sign for your store.
As for the types of things that a store can be liable for really isn't limited to anything. As a store owner, you're liable for everything! That doesn't necessarily mean that you're going to deal with legal issues and drastic things like being tied up in the court and those are certainly not reasons to shy away from starting a business.
With all of that said, however, I want so be very clear that I am not a legal professional so for any specific information you're going to want to speak with a legal professional in your area if you have any further questions about this. This is also our Terms of Service if you want to look over the specifics of our rules.
Since you're so young if you start now and run your business properly now you'll learn so much so by the time you're older the initial learning blocks will have been overcome so you can work to grow your business instead of learning to get started.
In that case, the first step would be to prove to your parents that you can be a responsible business owner. You could look at getting your parents on board the same way that you would look at getting an investor on board. Step one is to make a full business plan in order to prove to them that you can be responsible and to show them that you have a plan to run your business.
This document here is created to help aspiring entrepreneurs like yourself to build a functional business plan that you can bring in front of investors (or in your case your parents). Make sure you lay out what you want to do, how you plan on doing it, where you plan on getting the funding, who you plan on selling to, your timeline for starting your store/fulfilling orders, and as many other nitty-gritty aspects that you can.
— This whole guide is great and really worth a read, but one of the most important bits of information that you're going to want to take away from this is "How to create a budget"
Running a business can be daunting and an overwhelming task in the first place but I (as well as my other Shopify colleagues) are here to help you through the entire process.
If you'd like more help breaking down your business plan into steps to get it ready to show your parents please let me know and we can work step by step in order to create something that you can present to your parents.