The DB site will give you the total time from Calais/Boulogne through to Berlin.
It will give you the fare most likely from Paris, but you can try for the whole travel too. (If they do not have the price, they will mention 'fare abroad' or fare not known or something like that.
The SNCF site can give you the price from the coast to Berlin, I picked a random date and got a connection, Calais to Lille, Lille to Paris Nord, Paris Est to Berlin overnight. This travel cost from 76.90 € on the date I picked. That price depends on whether you can get a place in the night train for the date you want to travel. You might be willing to pay a little more, and get a couchette, often they are €20 more if you book early. The full price is more that twice that, but if you book ahead you can almost always pay less than full price.
I got this info on the SNCF site in French ( http://www.voyages-sncf.com/ ), you need to be able to read French to check the conditions, but if you do, it is the best site for the best prices. Collect your ticket in France, or use seat 61 to find the best seller for you.
The English version of the site sends you to: http://www.tgv-europe.com/en/
It finds the same connection, I am not sure whether the prices are the same, I have had times when the prices were higher.
The seat 61 site has a lot of information, but the fare info is mostly rather general.
It has details on where to buy the ticket you want, so it is always useful to try.
The travel time is about 18 or 19 hours, depending on which connection.
In Paris, the two stations are side by side, so you will not have to take the Metro, not will you have to reserve much time.
If you do not live near Dover, travel with the Eurostar will be a good alternative. The same sites will tell you all about it when you enter London or one of the other stations, as departure point.
There are connecting buses between the stations in Dover and Calais and the ferries, running at a regular schedule, and when I traveled with them two years back, they did cost €1,50 in Calais and a like price in England.
Select the station Calais Ville, as the other Calais station is much farther from the ferry port and does not have regular buses. You can also try Boulogne, if they still run ferries there.
PS:
I forgot to give you a clickable link to the German site:
http://www.bahn.de/international/view/en/index.shtml
I did run a short search on the connection for you and found several day connections, from impossible early to useful, the fastest taking about 8 and a half hours, so worth checking if the overnight trip does not attract you.
But indeed, the site can not find the prices in the automated system.
You can split the travel, do the part to Paris by the French site, and from there on the German site.
It can find the prices from Paris, but not after the timetable change early December.
The staff at the office in Germany can do the whole travel, and also in the new year.