How many elastic IPs (publicly visible) can be attached to single instance?
If you are running in VPC, yes you can. You need to provision extra network cards. From the Documentation;
Q. Can I assign one or more Elastic IP (EIP) addresses to VPC-based Amazon EC2 instances? Yes, however, the EIP addresses will only be reachable from the Internet (not over the VPN connection). Each Elastic IP address must be associated with a unique private IP address on the instance. EIP addresses should only be used on instances in subnets configured to route their traffic directly to the Internet Gateway. EIPs cannot be used on instances in subnets configured to use a NAT instance to access the Internet.