It rather depends which country you're referring to, but the British monarch in 1806 was King George the Third.
who was the last UK monarch of the 1800's
The longest reigning monarch in Thailand is His Majesty King Bhumibol Adulyadej.
The reigning monarch was James the first
victoria
Queen Victoria was the reigning monarch of UK in 1900, until she died the following year.
No, The reigning monarch can not choose the next monarch.
Queen Elizabeth II.
house of hanover
She is the longest reigning British Monarch ever having recently surpassed Queen Victoria's 64 years on the throne.
It was Queen Victoria
That would be a King or Queen.
The eldest son of the reigning monarch becomes king when the monarch dies. If the reigning monarch has no sons, then his eldest daughter becomes queen. However, the law has just been changed so that the eldest child of the reigning monarch becomes the new monarch on the death of the parent regardless of whether it is a boy or a girl. In practice, as Prince William's wife has just given birth to a boy, it will be at least 80 to 100 years before there is another female monarch.
When the previous reigning monarch dies, at that instant, the next in line becomes the new monarch - this is the accession. At some point in the future (after the old monarch has been ceremonially buried and after a period of morning), the new monarch, at a ceremony, makes promises to their subjects to rule justly and is crowned. At the the point of coronation the monarch becomes the new reigning monarch.