Signature-based Analysis -Heuristics/Anomaly-based Analysis

and which security product can do following

accurately profile web applications in order to provide threat correlations across multiple tiers from the network level to the application itself. Correlation rules incorporate all security elements to detect complex, multi-stage attacks

and Which security product can do following

detect anonymous proxies and allow to block them as per requirement

Which security product can do following

alerting facility via SMTP & SNMP traps as well as capable of integration with SIEM or pushing following type of logs to an external server. -System Logs -Access Logs -Audit Logs

seems you are trying to complete a RFP via dev central, while possible wouldn't it be wiser to contact your local F5 sales about this?

in general this feels like the ASM module with IP intelligence for the anonymous proxy part. if it will be exactly up to the task is difficult to predict without full knowledge, but the basis is there.