Of course they are. There is simply no way to prevent them from participating, except not allowing them access to computers.
The network is, last but not least, designed in such a way that nobody, no government, and no police, can prevent anybody else from participating. In particular, there are pseudonymous accounts, and these accounts do not give any information about the age.
The aim of the network is to allow you to find information about others - potential clients, friend, or cooperators. If the potential client has given information about his age, and appears to be a child, it may be reasonable for you not to sign any contracts with him. But this is your personal choice.
If children violate their contracts, their arbiters have established this fact, and the penalty is an entry in the black list, then there will be such an entry in the black list. And it will remain there forever.
But, of course, there are no automatical consequences. The black list simply contains information about some facts. What follows, for you, from the simple fact that somebody has violated a contract at age 8? That he is unreliable today, at age 20? Of course, not. So you will ignore this fact as irrelevant. So will everybody else with common sense.
One of the advantages of the network is that you can use robots (computer programs) to search for reliable people. These robots will, of course, also look into the black list, if there is a record about a person which otherwise seems reliable. But such robots do not have (yet) much intelligence. They can use only sufficiently simple criteria for evaluation.
Fortunately, the age is a simple criterion. If you are not a pseudonym or hide your age for whatever personal reason, your age will be known. The record in the black list will contain information about the other possibly relevant dates - the date you have signed the contract, the date you have violated it. So not only human readers, but even robots can exclude records about children from consideration. .
But what is the age of legal responsibility in this case? This is your decision. Your robot will have some "preferences" menu where you can define your own preferred age of legal responsibility.
And if this does not satisfy you, all you need is a better program, which gives you more freedom of choice - say, different ages for different types of violations, or degrees of responsibility, where an entry in the black list from age 15 does not lead to exclusion, but only adds some negative value.
As a consequence, there is no "the" age of legal responsibility. There are different opinions of different people about this. If you have violated some contract at age 13, the number of people who will boycott you because of this will be small, and it will increase with your age.
On the other side, if you are only 13, there will be a probably equally small number of people who agree to make contracts with you.
How much that matters, is another question. If your environment is full of people who think that a 13 years old is responsible enough, you will find lot's of people who make contracts with you. But it will hurt you much more if you violate a contract at age 13 - all those people in your environment will probably not ignore this record, and those who think that legal responsibility should start only at age 21 may be far away and not interested in cotracts with you for other reasons.