The documentary says "over 100,000" boys under the age of 15 were enlisted in the Union Army. This is far too high as the number should be closer to 1,000.
No white flag was raised over Fort Sumter. The flagstaff at the fort was shot down, so a man with a white flag was dispatched to offer the surrender.
The King of Siam never offered (and thus Lincoln never declined) a herd of "War Elephants." He did, however, offer to send some domesticated elephants to US president James Buchanan, to use as beasts of burden and means of transportation. The royal letter of 14 February 1861, which was written even before the Civil War started, took some time to arrive in Washington DC, and by the time it reached its destination, President Buchanan was no longer in office. Lincoln, who succeeded Buchanan, is said to have been asked what the elephants could be used for and in reply he said that he did not know, unless "they were used to stamp out the rebellion." However, in his reply dated 3 February 1862, Lincoln did not mention anything about the Civil War. The President merely politely declined to accept King Mongkut's proposal, explaining to the King that the American climate might not be suitable for elephants and that American steam engines could also be used as beasts of burden and means of transportation.