I am a beginner. Is there any place where I can play online and improve my game? I know of sites like Chess.com but unfortunately you have to pay for them. My parents won't allow me to spend money on it. What are the best free chess websites or apps?
The best completely free website I know of is Lichess. Personally, I use Chess.com. It's free to play on, and many of the features it has can be used by anyone. However, to gain full access to the website (e.g. the video library), you do need to pay for a membership. It is relatively inexpensive though—$100 per year, which is equivalent to $8.33 per month. (Other membership options are even cheaper.)
Many people still prefer Lichess, and it does have the advantage that absolutely everything is free. Ultimately, I think the best way to answer your question is to try out everything:
Proprietary (to gain full access, you need to pay):
Open source (completely free, and run by volunteers):
Note that even the chess websites that offer paid subscriptions often come with a money-back guarantee. If you're organised enough to cancel your subscriptions, then you can pretty much trial everything before coming to a decision.