There's a simple translation exercise "the one" with three pictures and with the correct answer "die Eins" illustrated by a large number 1. There's no discussion option at the exercise so I have to ask my questions here.
Why is it feminine? Why "die Eins" and not "das Eins"?
Does the German "die Eins" have the meaning of "the one and only" ? Or does it mean just "the number one" ?
All of the numbers are feminine in Hochdeutsch (High German), the dialect of German taught on Duolingo.
Hochdeutsch as taught here (or in 99% anywhere) is not a dialect. Its the standard form of german for writing. Its an artifical type and is different from the dialects of the group "Hochdeutsch".
All numbers use the feminine article. "Die Eins" does not mean "the one and only". It describes either the number itself or it describes the leading person/car in a race or any other competition (for the second use its more common to hear the phrase "Die Nummer Eins").
You could translate "the one and only" as "Die eine" (or die eine wahre or die einzige or several more). If "the one and only" refers to a male or neuter then it would become "der eine" or "das eine" (with other possibilities as mentioned above in brackets).