Using an SQL database offers numerous benefits for organizing and managing data. With an SQL database, you can:

1. Ensure Data Integrity: SQL databases provide features like constraints, triggers, and relational structure that help maintain data integrity and consistency.

2. Flexibility: SQL databases offer flexibility in querying and retrieving data using the SQL language, which allows for complex data manipulation.

3. Scalability: SQL databases can be scaled vertically (by adding more hardware resources to a single server) and horizontally (by adding more servers to distribute the load).

4. Security: SQL databases provide robust access control and security features to protect sensitive data from unauthorized access.

5. Reliability: SQL databases are known for their reliability, as they are designed to handle large volumes of data and high transaction rates without compromising performance.

6. Compatibility: SQL databases support standard SQL language, making it easier to migrate between different database systems if needed.

However, it's important to consider the specific requirements of your project, such as the volume of data, the nature of the data, the expected read and write operations, and the scalability, when choosing a database solution.

Traditional SQL databases are not designed for real-time data synchronization like the Firebase Realtime Database. However, modern SQL databases, along with additional technologies, can be configured to provide-time functionality.

1. Live Queries: Some SQL databases offer "live queries" that allow you to listen for changes to dataset results. This can simulate real-time updates but can have performance impacts and is not supported by all SQL implementations.

2. Publish/Subscribe (Pub/Sub) Model: You can also use a pub/sub model to push notifications of changes to clients. This often involves additional technologies and setup.

3. Using Real-Time Database Tools: Tools like RethinkDB, a NoSQL database, or Google Cloud Spanner, an SQL database, can also provide real-time functionality. They provide "changefeeds" or similar mechanisms to push changes to the client.

4. Middleware: Middleware applications can bridge your SQL database and clients to provide real-time updates. They sit between your database and clients to push updates.

Remember that setting up real-time synchronization in SQL may be more complex and need more infrastructure compared to using a service like Firebase Realtime Database, which comes with this feature built-in. Therefore, the choice them depends on your specific case, requirements, and resources.

To make a MySQL database behave in a real-time manner, you would often need to use additional tools or middleware since MySQL does not natively support real-time functionalities. Here are a few approaches that you could consider:

1. Polling: One simple but potentially inefficient method is by frequently querying (polling) your MySQL database for changes. While this does work, it can lead to unnecessary queries and load on your system, especially as your data grows larger.

2. MySQL Binlog: The binary log (binlog) contains a record of all changes to the database. It's primarily used for replication and recovery purposes. There are tools, such as Debezium, that can read from the binlog to achieve something close to real-time database updates.

3. Pusher Channels: Pusher is a service that allows you to send real-time updates. A hybrid approach involves combining a MySQL database with Pusher. Any changes to be broadcasted are sent through Pusher to the client.

4. Using Additional Middleware: Middleware like Node.js or Socket.IO can be combined with MySQL to provide real-time features. These act as intermediaries that listen for changes and then emit those changes to clients.

5. Third-Party Services: Other services like Google Cloud SQL or AWS RDS utilize additional features to provide real-time updates.

Making MySQL behave in real-time can be complex. It's important to consider your project's needs when deciding whether the complexity and potential overhead of the above options are warranted.

Yes, PostgreSQL, a popular open-source relational database management system, does support real-time data synchronization. PostgreSQL has several features that enable real-time data updates, including:

1. Streaming Replication: PostgreSQL provides a built-in streaming replication feature that allows you to replicate data from one server to another in real-time. This feature is particularly useful for disaster recovery, data aggregation, and other real-time data synchronization scenarios.
2. Logical Decoding: PostgreSQL's logical decoding feature allows you to decode queries and logs in real-time, enabling you to track changes to the database and retrieve useful information.
3. Row-level transactional replication: PostgreSQL's row-level transactional replication feature allows for real-time synchronization of transactions across multiple servers, enabling you to maintain a consistent view of the data across multiple systems.
4. Event Triggers: PostgreSQL's event triggers allow you to define actions that are executed in response to specific events, such as changes to the data. These triggers can be used to update the data in real-time.5. TimescaleDB: TimescaleDB is a PostgreSQL extension that adds real-time data analytics and time-series functionality to the database. It allows for querying and analysis of time-series data in-time, making it ideal for use cases like IoT data processing financial market analysis.

These features make PostgreSQL well-suited for real- data synchronization applications such as online gaming, live analytics, and real-time collaboration tools. While PostgreSQL does support real-time data synchronization, the complexity and scalability of the application will still depend on the specific use case and the requirements of the project.