A Mainframe is a high-performance computer used for large-scale computing purposes such as bulk data processing and enterprise resource planning. Key features include reliability, scalability, extensive I/O capability, and high security.

Job scheduling in a Mainframe environment is typically managed using job control language (JCL) and scheduling software like IBM's Job Entry Subsystem (JES), Control-M, and CA-7 to automate and plan the execution of batch processing jobs.

To optimize a COBOL program, I would focus on efficient coding practices such as minimizing I/O operations, using appropriate data types, optimizing SQL queries if databases are involved, and leveraging compiler optimization settings.

CICS (Customer Information Control System) is a transaction processing system from IBM used for developing and executing online transaction applications. I use CICS by defining resources through its online interface, writing COBOL programs to handle transactions, and debugging using tools like CEDF.

Batch Processing involves executing a series of jobs in a batch without manual intervention, suitable for executing repetitive tasks. Online Processing, on the other hand, involves processing transactions in real-time, allowing for immediate data input and output, typical in applications like banking.

Data integrity and security on a Mainframe are ensured through several means, including access control mechanisms like RACF, data encryption, regular audits and monitoring, redundancy for data protection, and strict adherence to security policies and practices.