You are getting the reply from Outside Interface IP or some external IP.are you using ICMP access-list on the outside Interface ?

Hi,Are you connecting the Internet link directly on the ASA or it is behind the Router .I think its an ARP issue.try to clear the ARO cache of the Router

HI,No Static Public IP is require at Branch location.But your CO shoulg have fix Public IP on ASA Internet facing Interface.You can use latest Cisco VPN Client software.

Yes you can upgrade to v6.3

HI,You will be requiring CSC Module for URL Filtering.