Nimbostratus
Nimbostratus"When does it become enforcement ready? After the enforcement period we have mentioned under policy building?"
Voila. It depends on enforcement readiness period as set in your policy settings. By default it is 7 days.
"And when does the entities state move from staging to having suggestions? Does it depend on the tighten policy setting under learning and blocking settings?"
Learning suggestions are raised only if you have enabled Learning Mode in policy settings. When enabled, and a request comes in which gets blocked, then a suggestion may be raised. This is basically self-intelligence of BigIP whereby it tries to guess what's best action for you to take. Personally I do not trust this feature. You can see a better description here if you Ctrl + F for encounters of "learning suggestion" and "learning mode": ASM Ops Guide
NimbostratusIf you have ASM enabled:
Make sure the following signatures are Enabled and Enforced. In particular, 200000098 and 200001475 should be relevant for search input fields.
XSS script tag (Headers) 200000097
XSS script tag (Parameter) 200000098
XSS script tag (URI) 200000099
XSS script tag end (Headers) 200000091
XSS script tag end (Parameter) (2) 200001475
XSS script tag end (URI) 200000093