I want to build a web application with MySQL database.
When more users will visit my site, more database queries will be initiated and the response time will increase.
- Is there a limitation for the number of users who can query MySQL?
- What are the ways to handle heavy duty traffic to queries?
- How do think sites like Facebook handle this problem?

1. Number of connections are controlled by MySQL configuration parameter max_connections.
2. Use caching in your application and MySQL. Design your DB in such a way which requires minimum JOINs to fetch data. This is also known as denormalization. Write optimize queries, avoid SELECT * sort of quereis and properly index your data.
3. They adopt all the techniques which are mentioned above and as well as some others which is not mentioned here

They have multiple web servers and database servers, you can say server farms.

Read this article to optimize your application.