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Type D: National visa or visa for research purposes.
You are required to stay in Germany for longer than three months within the six-month period after your first entry. Any person in possession of a National visa and valid travel documents are permitted to move freely in the Schengen area for up to three months in any six-month period.
NOTE: A Type D National visa can be converted into a residence permit after entry into Germany. However, you must still actively apply for your residence permit after entering the country.You will need to convert your visa into a residence permit within three months of arriving in Germany.
It shouldn't be a problem for you to travel inside Schengen countries as I rarely see visa check-in airport if you are travelling inside the EU from any Schengen country. Your plane ticket is enough if you are flying else you can simply use a train or other means for travel where they don't go through visa unless you don't commit any illegal activities.