What should a 11-17 years old Buddhist do?

Children, believe it or not, are smarter than adults. It is easier for a child to learn a second or third language than it is for an adult. (Which incidentally is a commendable endeavor worthy of a Buddhist practitioner or scholar of any age.) Children can memorize memorable sutras, either in English or in the original, just as well as adults, or better; they can maintain yogic postures just as well as adults, or better. The right question isn't necessarily, what Buddhist practices are suitable for children, but rather, what is a SMART, reasonable goal for a human being to hope to attain in his or her lifetime. What goal would be Specific, Measurable, Achievable, Relevant, and Time-bound?

Is it reasonable to say, "I hope to become a Bodhisattva/an arahant in this current human lifetime?" Or, "I hope my child or this gifted student in my middle school class becomes a Bodhisattva/an arahant in his or her lifetime?" Put another way, if a talented guru or motivational speaker, someone clearly more intelligent and accomplished than yourself, claimed to have attained Buddhahood in his lifetime, would you immediately leave everything behind to follow that guru?

Or would that instead be a dangerous red flag?

Whatever is a realistic goal for yourself, as an adult following the Buddhist path, would likewise be a realistic goal for your child, being your flesh and blood. Whether that goal is to be a "stream entrant", or simply to pay respects and give ear to a teacher. Or simply to better apply one aspect of the Eightfold Path: maybe, Right Livelihood, Right Speech, or Right Effort. Or one of the Six Perfections: charitable giving, conscientiousness, graciousness....

Teach the child whatever your goal is, but the child must choose his or her own goal. Children should preferably be exposed to a wide range of Buddhist doctrines and "book learning" so that after they mature and become more self-critical, they can apply Buddhist wisdom to grow their greatest strengths, but also to attack their greatest weaknesses.

Sure they can only if they followed the perfect path, and for my understanding step away from present society will massively helpful for that goal. And Buddhism is not only for adults, it's for all HUMAN BEING.

To give a direct answer to the question, "No". Buddhism is not only for adults. Buddha has preached that a child who is able to make a crow fly away is in the suitable age to be a monk. and there are evidence in the scripts about arahat bikkhus who attained arahat at the age of 7.

No Buddhism isn't only for adults.
If Buddhism were only for adults then there weren't be zens.
Here you can see there are zens and so lay children can also practice Buddhism.
I'm single yet but I want my kids follow Buddhism I'll teach them Dhamma.
At little age it'd be nice to cultivate their mind so they'll be best practitioners when they will became an adult.
It's best to shape their mind.
It'd be really best thing to teach them Dhamma.

I've heard from a Bhante, that at the age of 7 only does the brain fully develops as to understand the true phenomena of the universe. So anyone of 7 years of age and above the age of 7 can become an Arahat.

Notable examples include, Arahat Rahula Thero, Arahat Seevali Thero and Arahat Sopaka

Only in certain special cases at the time of the Buddha have there been Arahats younger than 7 years of age.

Buddhism is for everyone! You can also become an arahant at any age.

Nirvana is present in every moment. Every moment is an opportunity to observe Nirvana. Every moment is an opportunity to become enlightened!

Starting as young as you are is wonderful! You are setting yourself up well to reach enlightenment this lifetime! You should be very proud of yourself!

Some (I presume most) Buddhists are taught to start their practice when they are children.

Who was the youngest Arahat? discusses references in the suttas to young (e.g. 7-year-old) Arahants.

The Ambalatthika-rahulovada Sutta (MN 61) are instructions which the Buddha gave to his son, Rahula, when he was 7:

1. Don't lie
2. Look at ("reflect on") what you do, what you say, what you think -- before, during, and afterwards -- to know whether it leads to affliction or not.
3. This type of reflection is the one way to "purify" the three kinds of actions (bodily, verbal, and mental)

According to the canon, Rahula too became an arahant (not immediately -- by about age 20).

No, wisdom and needed merits are not a matter of age. And a young tree can be bend easy, while an old is hard to change.

As a child, being provided by all needed to live on (all totally voluntary by others = much debts and required gratitude for it), one can easy life a holy life and attain Sainthood, if in good guidance of what is good and listen to it.

Seeking out for good monks (keeping the original rules, do not act as lay-people servants and live with lay people), associate with them, render service, listen and if having possibility seeking for being allowed to go forth by oneself: e.g. ordain.

If one is female, a girl, one should not go alone without one's parents, or other male protectors (allowed by father and mother) and approach monk/monks alone. Also should not join even groups of mixed gender and always look out for female groups, tend to mother and possible seek out for nuns our female practicing groups, if very trustful male attendant can be not found or listen to the Dhamma on more public occasions and events to be protected by the group.

In no ways a young person should accumulate debts or waste his merits/wealth for useless things. The sooner meeting and associating with noble people and with deed love listen and follow their advice, the more secure would a young persons path to highest gainings be.

If not accessible, such real friends yet, focus on right view, fulfill all duties toward parents, teacher, elders, stick firm to the basic precepts and practice generosity. Giving the causes, all effects come by its own: patience is all that is required.

They should in no way lie without dependency and walk around thinking "I can get it somewhere else..." and act very strong bond to their "father", "mother" not violating there duties (which of cause does not include to act against the basic precepts).

Depending on parents and owing a lot of debt toward them, they should ask them whether the are allowing to associate with someone else and depend (also if particular) to them. This includes also asking parents if they allow to join a internet community. (it's totally improper how exchange and "against good moral", for example, acts careless in giving those under protection ways to act outward their relation. A child is not what is called "vested with legal capacity" and certain disclaimer do not protect especially a legal person of "full legal capacity".).

So possible start to ask your parents if they agree that you came here! And follow what they advice.

Seeing a young man acting according his known rituals, the Buddha explained him the detail meaning and gave him the lay-mans rules: The Layperson's Code of Discipline.

At the end here maybe a short story about "The lucky young monk" and the Arahat Novice Ven. Tissa.

It all depends on the individual's effort and potential, and how much Dhamma they've been cultivating since countless previous lives. Sorta like child prodigies who can become accomplished medical doctors, mathematicians, or musicians in their teens.