Are there any official online tests for ADHD from gov or pediatrics websites?

No.... But. There are no official online tests from the government or aap recognized websites for the diagnosis of adhd. It's diagnosed predominately from careful history taking and in-office observation. However, there are questionnaires available online that can assist your doctor in making the diagnosis. One of the more widely used is the nichq vanderbilt which has parent and teacher versions.
Not test, but survey. Diagnosing adhd requires input from parents, teachers and pediatricians. Although you can find surveys online that can suggest if your child is at risk, a formal diagnosis would require a medical evaluation. Please voice your concerns to your pediatrician who can help start the process.
No. Adhd is a clinical diagnosis. There is no test for this disorder, not online, not in the doctor's office.
Many surveys. There are many available surveys that are used by pediatricians, neurologists and psychiatrists. they include the Connors Rating scales, Vanderbilt Rating scales and many others. Ask your pediatrician about what they use.
Vanderbilts. There are MANY online resources with scientifically based tools to help evaluate for ADHD. Look for sites that use either Vanderbilt or Connor's scales, as these are likely to be most reputable and can be completed and taken to your physician for further interpretation and treatment. Here is a great resource for you: http://www.chadd.org/Understanding-ADHD/Parents-Caregivers-of-Children-with-ADHD/Evaluation-and-Treatment/Evaluation-and-Assessment-Tools.aspx.
Yes questionnaires . These questionnaires are never diagnostic. Only a doctor can make a diagnosis and treat adhd. See nih website: http://www.Nimh.Nih.Gov/health/publications/attention-deficit-hyperactivity-disorder-easy-to-read/index.Shtml. Also chadd.Org. The tests for adhd are much more complex than questionnaires. Visiting website is beginning. Then see your doctor if you suspect you may have it.
ADHD. There are diagnostic questionairres that we Pediatricians use . This is a general professional advice limited to USA patients based on information provided and is to be verified by a Physician familiar with the patient.
Yes Pedi./CP sites. There are a number test for adhd--Iowa ADH rating scale, the the ADHD rating scale, Connor ADHD rating scale, the SNAP. Child and Adult versions of rating scales. American Pediatric Association site has a numbe rof suggested test for ADHD. Anothr test used created by Connor is the Continuous Performance Test.--a computerized program used to test certain aspects of ADHD.