Linux behind a cisco router

Dear All,

I have worked with xDSL routers working in bridged mode, and linux behind them working as a Firewall utilizing IPTABLES. My question is, how this will change if the xDSL router is replaced with a Cisco Router?
I mean to ask that, can I assign a public ip on the linux machine, which is behind the Cisco router? Do I have to do natting/port forwarding on the Router ? One ethernet on router is directly connected to linux machine. Can I utilize some packet analyzer or sniffer to find out what goes on during this type of communication?

Thanks for taking your time to read this.
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