Select Specific Monitor for Health Monitor "Availability Requirement"

There is no way to do that - you either specify that all monitors are required, or a minimum number of monitors of the available monitors are up.

ltm pool http_pool {
    members {
        10.0.0.145:http {
            address 10.0.0.145
            session monitor-enabled
            state up
        }
    }
    monitor min 2 of { tcp gateway_icmp http }
}

or

ltm pool http_pool {
    members {
        10.0.0.145:http {
            address 10.0.0.145
            session monitor-enabled
            state up
        }
    }
    monitor tcp and gateway_icmp and http
}

You cannot mix the min key option with the and option in the configuration.