Well generally I would have the ISP router/modem configured as a bridge device with no IP address at all and configure the public IP address assigned by the ISP directly to the ASA "outside" interface. If the ISP only provides you with DHCP IP addresses then you would need to configure the "outside" interface to get its IP address with DHCP rather than configure the IP staticly.
Are you sure about the gateway address?
For the NAT configuration format we would need to know the device current software level which can be checked with the command
I guess it would be easier to see the actual configurations of the ASA in their current form and then we could suggest what might need correcting or what you should check.
I am sorry but I am not sure I really understand the question.
With regards to routing and forwarding traffic the ASA generally looks at its routing table that can be viewed with "show route" command. But the NAT configurations especially in the 8.3 (and above) software levels can override the routing table when ASA is choosing the output/egress interface for the traffic.
Table of ContentsIntroductionVersion HistoryPossible Future
UpdatesDocuments PurposeNAT Operation in ASA 8.3+ SectionsRule Types
Network Object NATTwice NAT / Manual NATRule Types used per SectionNAT
Types used with Twice NAT / Manual NAT and Network Obje...
Table of Contents Introduction:This document describes details on how
NAT-T works. Background: ESP encrypts all critical information,
encapsulating the entire inner TCP/UDP datagram within an ESP header.
ESP is an IP protocol in the same sense that TCP an...