Yes, while not fully harmonised, it is a safe assumption for the countries you mentioned. It follows from a proposal to the EU members in 2007 (resubmitted in 2011)...
PNR data is information provided by passengers during the reservation
and booking of tickets and when checking in on flights, as well as
collected by air carriers for their own commercial purposes. It
contains several different types of information, such as travel dates,
travel itinerary, ticket information, contact details, travel agent
through which the flight was booked, means of payment used, seat
number and baggage information. The data is stored in the airlines'
reservation and departure control databases.
Many states access PNR data for the purpose of fighting serious crime
and terrorism. PNR data has been used manually for almost 60 years by
customs and law enforcement authorities around the world.
Technological developments have made it possible to use PNR data more
systematically for law enforcement purposes.
Source: Passenger Name Record (PNR)
The current state of affairs is most of the member states have passed their national legislation and have either implemented the proposal or in an advanced test phase.
Currently up to 16 EU countries have decided to collect PNR data,
according to Timothy Kirkhope, a British Conservative MEP who steers
the file through Parliament. But because there is no EU framework, he
said, “airlines have no clarity on how to process the data, and
passengers have no clear EU-wide rights to protect booking information
such as credit card details, seat number and emergency contact”.
Statistics from the Parliament show that most EU countries already
have their own PNR systems in place. In 2013, the European Commission
spent €50 million to start domestic PNR collection in 14 member
states.
Source: Passenger name record law passes first hurdle in Parliament
The UK enacted the legislation in 2008 in the form of a Statutory Instrument: The Immigration and Police (Passenger, Crew and Service Information) Order 2008
In 2010, the European Commission issued a communication on the sharing of this information with non-member states: On the global approach to transfers of Passenger Name Record (PNR) data to third countries
Earlier this year, 16 July 2015, the proposal was put to a vote and carried by a slight majority. The full EU framework and harmonisation by members will presumably be complete in 2016.
...a Dutch national travelling on a Dutch passport via a German international airport to an Asian country be logged?
Having said all of that, we turn to your specific question. The Netherlands has an EU compliant PNR system in place and is still formally in a testing phase. Germany has not yet developed an EU compliant PNR, but uses the version they implemented before the proposal was made. So the answer to your question is still 'yes', but data originating in Germany is not kept in an EU compliant format.
If yes, for how long is this information retained?
The main legislative instrument at EU level governing this field was
the Data Retention Directive, which was adopted in November 2006
following the Madrid terrorist train bombings in 2004 and the public
transport bombings in London in 2005. These resulted in a text which
gave room for different applications at national level and which did
not guarantee a sufficient level of harmonisation.
Source: Passenger name record law passes first hurdle in Parliament
does it make a difference if the automated ePassport gates are used rather than the human officers?
No difference, the border inspection process does not play a role in the harvesting of information. Per the proposal the information is collected at the booking and reservation stage.