What are some potential low-cost businesses that can be started and operated by a teenager?

I would say anything that comes in handy or something that will help your fellow students. As a teenager you might want to sell customised cards or stationary items or designed tshirts. Or if you are passionate about cooking, you might sell small food items. These will cost you little, and gradually you can increase your business. You can even take help of your friends who might as well contribute to your start up. Marketing on social media is a great way to spread information about your business. Another startup idea can be to sell customised jewellery if you are good with crafts. 

I would recommend web development. More specifically WordPress setup. WordPress is very simple and there are thousands of themes available to suit any business. It is a blogging platform but I see so many businesses using WordPress as their main website. You simply guide businesses through setup process help them choose a theme & train them on how to use it.

As you get comfortable with WordPress, you can start customizing themes, or even writing complex plugins.Then slowly you can add more offering such as setting up Shopify, etc.

The best part about this business model is that other than minor hand holding you don't have to provide any time consuming technical support for the customer. If their website is down, they contact WordPress or Shopify etc.