Are there any general trends according to months? This involves astrology.
Assigning attributes to human characteristics based on their birth-month is virtually the same thing as by astrological sign, the difference in grouping is on average nine days. Astrology has not demonstrated its effectiveness in controlled studies and has no scientific validity, and is thus regarded as pseudoscience. Months are in fact more irregular as a distinction than star signs (month durations vary from 28-31 days).
Having worked in the music industry for 15 years, I can suggest a much more probable cause for the alledged Musician/December "correlation": it only lists famous artists. The success rate for artists a label signs is a fraction of the total signings. This has almost nothing to do with the musical mastery of an artist, but largely with the Zeitgeist of when they release something. Arguably, many of the best artists never become famous because they are ahead of their time. It is only (much) later that their brilliance is recognized. You have the same pattern with painters. Van Gogh was only recognized as one of the most influential painters of all time long after his death. The difference with music is that this recognition doesn't automatically translate into posthumous record sales and thus fame.
The ADHD/August article states:
In states with a Sept. 1 birth date cutoff for kindergarten entry, children born in August -- the youngest in their class -- had a 34% higher risk of ADHD diagnosis and a 32% higher risk of ADHD treatment than children with September birthdays
Which means the age difference between an august born child and a september born child in the same class is 330 days. The month by itself has nothing to do with ADHD risk, it is the combination with the legally defined cutoff. If the cutoff date would be June 1st, then the findings would likely be shifted to children born on May.