Is there a remote desktop software that allows desktop client to use multiple monitors against a remote laptop?

No, you do not need to be physically present for establishing a remote session. You can connect to a remote computer from anywhere in the world as long as both computers have an internet connection.

To safely disconnect from a remote session:

Use the logout or disconnect option in the remote access software. This ensures that any active sessions are closed, and no one can access the machine afterwards.
If using Windows Remote Desktop, click the X on the session window, or go to Start Sign out to end the session.
Make sure that all applications are closed, and your work is saved before ending the session.
These practices ensure smooth and secure remote desktop operations.

Yes, you can access multiple remote computers from one device, depending on the software. Tools like Microsoft Remote Desktop, TeamViewer, and Splashtop allow you to manage and switch between multiple remote connections from a single device. You may need to configure each computer separately, and some tools offer a management interface to keep track of multiple machines.

To ensure your remote desktop session is private:

Use strong passwords and enable multi-factor authentication (MFA).
Ensure the remote access software uses end-to-end encryption, like AES-256.
Use a VPN to add an extra layer of security when accessing a remote machine over a public network.
Disable clipboard sharing, file transfer, and other features unless necessary.
Always log out or lock the remote machine at the end of your session to prevent unauthorized access.

Data usage depends on the resolution and frame rate of the remote session, as well as the amount of interaction:

Basic remote access sessions with minimal activity can use about 500 MB to 1 GB per hour.
High-definition sessions, including streaming video or graphic design work, can use 2 GB or more per hour.
Reducing screen resolution and limiting video or graphic-heavy applications can help lower data usage.