!?? the ages of the kids do not correspond with their birth-years.

@1: I do not understand this question

@2-just read the conditions all sent out in order; NOT possible

As a former mathematician, I said the year they were in, not the year they finished :)

The meaning of my question is:

1. How wise is it for me to travel with my wife and 2 children?
2. Does anyone travel this way? If so, what are the suggestions?
3. How much does it make sense to travel with 2 children?
4. Is it very difficult to travel with children?
5. How many of the participants in such programs are single or student or traveling alone?
   What are your views and suggestions on this subject?

I meant this in question 1st.
In case if I give up traveling with my children and wife and want to travel alone, is there someone here to help me or anyone planning to travel? Where should I start?

In respect of planning your trip decide where you want to go. Google can help. Once you have an itinerary look at the timetable and maps to determine a sensible route, Lots of people travel with children you will just need to reserve seats on busy trains to ensure you are together or use regional trains where reservations are not needed. 

For children younger than 4 years of age when the trip starts and who can sit on your lap, you don't need a children's pass. Children who have turned 4 but not 12, and children under 4 who need a seat of their own, need to have a children's pass.

It is the child's age when you start the trip that matters.

1. Why wouldn’t it be wise 4 is a perfect number to travel by train. More than that can be a bit more difficult.
2. Plenty of people. Take enough entertainment options for your children, and don’t stay too long on the train. Better reserve a family car/compartment and avoid silent coaches, leave those for the people travelling without children. A lot of long distance trains have separate spaces for families with young children, in some (long-distance) trains there are even toys (like Railjet, and some Swiss and Scandinavian trains).
3. Similar answers as above.
4. That depends on your children I guess? I took a lot of groups of children on the train back in the days, as a youth organisation monitor. That was never a problem, although we drilled them a bit to always stay together, not to play in the station and on the platforms and they had a phone number with them in case they got lost.
5. Interrail is not a program, it’s a highly flexible golden ticket for train travel all across Europe and quite cost effective if you pick the right trains. You have many kinds of travellers, and you can travel in 1st or 2nd class. It’s not only young backpackers that use it. Families with kids, groups of grown-up friends, seniors,… I’ve all seen them use Interrail/Eurail.

Everyone needs a valid ticket to travel (= your Interrail/Eurail pass), so when necesary you can travel alone.

If you have a more detailed idea we can give you more concrete advice and give you suggestions which trains are nice to use if you want to travel with young kids and which trains require reservations.