DB Rail and Eurorail

DB, aka Deutsche Bahn, is the German national railway and operates most of the trains in Germany, except for a few private railways, and it sells tickets for those as well. Eurail (not Eurorail) is a ticket agency that is a joint consortium of all the rail roads in Europe that markets a pass. It does not operate any railroads.

If you want to look at schedules, DB shows all the schedules in Europe. Their website is easy to use to quickly look at schedules. www.bahn.com.

The answer is the first choice to buy tickets is from the company running the trains.
DB = Deutsche Bahn = German Railways. They operate ~90% of the trains in Germany, so that is the place for tickets within, to or from Germany. That website also includes the small local rail companies in Germany.
Rail Europe is a ticketing agency in North America, who don't run any trains. They don't sell all tickets, and frequently have markups on the ones they do sell.
Eurail is a pass (multi-trip ticket) marketed to tourists outside Europe. It sells on convenience, but is usually more expensive than buying normal tickets, and you still need to pay supplements ("Reservation" fees) for many long-distance trains.

Each country has a different rail company, and some have many. And each has different ticketing policies. It can get complicated (just think of the number of airlines there are, and differences between their ticketing systems).
For a primer on how to buy tickets, see here: https://www.seat61.com/Europe-train-tickets.htm

Norway airport to Oslo city centre - local tickets like these are best bought at the station on the day.
Amsterdam to Rotterdam (local area) - tickets in the Netherlands (except High Speed trains) do not offer a discount for advance purchase. Again easiest to buy on the day.

Eurail used to sell tickets, but they no longer do. They now only sell rail passes. RailEurope sells tickets, marked up over the prices the individual national rail companies charge. Although Eurail creates the Eurail passes, they sell them wholesale to resellers who are free to charge whatever prices they want to. RailEurope usually undersells Eurail.

I haven't checked into Loco2, but for Germany Trainline marks up tickets about 8% over what the Bahn charges. If you can get tickets from the Bahn, buy them there.

Neither the Bahn nor Trainline sells tickets for regional travel inside Verkehrsverbünde (metro districts), and these ticket are almost always better priced than tickets for long distance trains between the same stations, which the Bahn does sell. Finding those tickets is complicated, but there are people here who can tell you how to get tickets for regional trains, S-Bahn, etc within Verkehrsberbünde. Ask us.

The regional / local area tickets, I would buy at the train station. As for the long distance like Berlin to Prague, I would purchase ahead of time. Once you have your schedule fully fleshed out. We used to make use of the passes, but now we travel as described above.

Why do you want to buy a ticket from Hamburg to Rødby?

Berlin - Prague

The fastest train connection for Berlin to Prague is 4½ hrs with the direct EC through Dresden. The Bahn sells totally flexible (non-train-specific) tickets for 71,80€ ($80.70) or, for the 10:59 EC on a date in mid-May, a non-refundable, train specific Super-Sparpreis ticket is 44,90€ ($50.47). Trainline shows $84.80 for the flexible ticket and $54.63 for the Super-Sparpreis ticket (includes Trainline's booking fee of $1.60). Loco2 charges $83 and $52 respectively for the same tickets.

However, it you get your ticket from the Czech Rail website, www.cd.cz, the price is 632 Kc (about $28).

It pays to check the fares on the national railline websites.

And, RailEurope sells the same tickets for $57 and $88 respectively.

BTW, since both Trainline and Loco2 are located in the UK, if they charge you US$ for the bill, isn't that DCC (Dynamic Currency Conversion)?

I believe you can specify paying in EUR at both Trainline and Loco2. That is how you can tell if they are marking up the tickets. I speculate that Trainline began charging fees to cover the transaction costs of all the triple reward point credit cards Americans use.

I want to take the train from Hamburg to Puttsgarden and go over with the train on the ferry (that is why I want to go from Hamburg to Rodby), is there a suggestion on a different way to Copenhagen Denmark?

If you want to take the train from Hamburg to Copenhagen via the Puttgarden-Rødbyhavn ferry you can just buy a ticket from Hamburg to Copenhagen from Deutsche Bahn. It will include the ferry and any potential train changes.

If you choose a Eurail Global Pass, then you're choosing a certain number of calendar days for traveling, such as 3, 5, or 7 travel days within a month are the cheaper versions. So for price comparison, it makes a difference whether Berlin-Prague roundtrip is on one day or two days, whether you're stopping overnight in Hamburg or just passing through, etc. No other train travel in Norway or elsewhere?

Thanks Laura, we will travel to Prague from Berlin (spending first night in Berlin) and spend overnight in Prague and return the next afternoon to Berlin. We will spend another night in Berlin, then travel to Hamburg and take the train from Hamburg to Puttsgarden to Rodby Denmark (train goes onto the ferry). We will take the bus from Rodby to Copenhagen Denmark (from my research that route looks ok). We will spend a overnight in Copenhagen, then the next evening we will fly to Oslo Norway and spend a night in Oslo. We will take another flight from Oslo to Amsterdam and spend 3 nights to explore Amsterdam and surrounding areas.

Yikes! Is this the Amazing Race, or a salesman's road trip? All your time traveling and checking in and out of hotels and no time being there. Too each his own, I guess.

Your plan is simply too rushed in my opinion, you will end up spending more time in transit and checking in and out of hotels than actually seeing anything in the places you visit. I would cut at least two of you destinations and spend a minimum of 3 days in each city you visit.

I also wouldn't do these quick stays in such interesting cities. A train ticket from Berlin to Copenhagen, including the two connections, takes 7.5 hours and costs anywhere from €40 to €155 per person in 2nd class, depending on how soon you buy it. (Your other post says you're traveling in September, so you still have time to grab the better rates.) Even so, you can normally fly nonstop on EasyJet, Norwegian, or other airlines for less; check your date at www.skyscanner.com.

Is your goal to see Europe, or European transit? If you want to see planes, trains, buses, boats, and not much else, you have a great plan. Otherwise, PLEASE stop and breathe, and figure out what you want to see, and actually spend some time there. Then, with a re-done itinerary, you can figure out if any kind of train pass makes sense. It probably won't, as you can use a combination of advance purchase discount tickets for longer trains, local transit deals for shorter trains, and flights for some segments.

For instance, it's about 5 hours on a train from Berlin to Prague. So, going there one day and back the next, with only one night in between, you have only a few hours of actual sightseeing. The rest of your trip is similarly short-changing wonderful places for lots of transit.

We are staying in Berlin two nights and Amsterdam 3 nights (those are the places my friend is focusing on). I have been to these places before (flown directly the city) and have lived in Europe. It has been 3 or 4 years since I have used the rail system. i just returned from Europe in a different part (stayed two weeks), I am always traveling (my friend does not have time I have to travel).