You will need around an hour to clear immigration, customer and to get you luggage. With some time buffer you should take a train about 1,5 - 2 hours alert your arrival.
The easiest way is to buy the train tickets in advanced and have your itinerary printed out. Just remember there are different types of tickets available from Deutsche Bahn. The cheapest tickets don't give you any flexibility. You can only take the exact train that is printed on the ticket. The more expansive tickets give you the flexibility to take earlier or later trains on the same day. Easiest way to get form Düsseldorf to Bonn by train is the Regional Express train which takes an hour to Bonn without changing the train. Just book your tickets
https://www.bahn.com/en/view/index.shtml . Search für Düsseldorf Flughafen - Bonn Hbf . Be aware Düsseldorf Airport has two train stations. One is Düsseldorf Airport Terminal right under main building the other one is just Düsseldorf Airport a bit outside of the terminal. I recommend to take a train from Düsseldorf Airport and not Airport Terminal. You need to take the terminal shuttle train to get there. The shuttle will take around 5 minutes to get you to the train station.
Yes, you should have EUR with you. While you can use your credit card for a lot you will also need cash at many places, especially restaurants tend to prefer cash or just debit cards but not credit cards. There are exchange booths at DUS airport.
I thought metal implements are non-magnetic and do not trigger the metal detector? If they do you would need some kind of medical notice form your doctor to get through security.
It does not matter if you fly to DUS or FRA.