This aristocratic family is:
the Noble Gases from the Periodic Table of elements.
Each line of the puzzle's pattern works as follows:
The last two digits of the year are the atomic number of another (non-noble) Periodic Table element whose shortform symbol can be combined with that of one of the seven noble gases to form the name of an animal.
In 1904, the first person got married. The couple adopted a Bear.
Element 04 is Beryllium (Be). With Argon (Ar) these two symbols combine to make BeAr.
In 1913, the second person got married. The couple adopted a Lark.
Element 13 is Aluminium (Al). With Krypton (Kr) you can make lArK.
In 1952, the third person got married. The couple adopted a Tern.
Element 52 is Tellurium (Te). With Radon (Rn) you can make TeRn.
In 1983, the fourth person got married. The couple adopted an Ibex.
Element 83 is Bismuth (Bi). With Xenon (Xe) you can make iBeX.
In 1987, the fifth person got married. Which animal did the couple adopt?
Element 87 is Francium (Fr). The noble gas thus far unused whose symbol can form an animal name when combined with 'Fr' is Oganesson (Og), giving us FrOg.
In which year did the sixth person get married?. The couple adopted a Hare.
The noble gas involved in this question must be Helium (He). Since the 'aristocrats' are all marrying commoners (i.e. non-nobles), we can exclude Argon (Ar) from consideration, and instead the other element involved here must be Radium (Ra), which as element 88 in the Periodic Table means the marriage occurred in 1988.
What is the name of the unmarried person?
The 'unmarried person' - i.e. the only noble gas remaining - is Neon! (Sadly for them, they may have had two chances to wed in 1973 and 1985, but might have considered their potential matches a little too old-fashioned!)
So in summary, the three questions yield the answers:
A frog, 1988, and Neon.
