Things that a 13 year old can do at home alone are do crafts like origami, drawing, writing or other creative activities.
Other things a 13 year old can do at home alone are study, read books, learn a new skill online like language skills or learn how to play an instrument.
You can also watch TV or Watch YouTube videos, listen to music, or even make YouTube Videos.
Engaging in physical activity like playing basketball, soccer, going for a walk, going for a bike ride or even going for a run can also help a 13 year old stay busy and healthy to help pass the time.
You could also clean your bedroom or organize your bedroom.
Or do a home workout, shoot hoops if you have a basketball hoop or practice yoga.
You could also take a warm bath with some bubbles to unwind and relax.
Or catch up on books, read magazines, browse your computer or phone.
Making slime, starting scrapbooking or making a paper fortune teller are also good activities for a 13 year old at home.
Even sweeping or vacuuming the floor if needed or just going outside if it's warm and sitting outside to get fresh air is also good.