Yes; the digits repeat themselves after every 6000 decimal places.
No; only women, not numbers, are unfortunate enough to be periodic.
Maybe; not enough digits of pi have yet been calculated to know if they start eventually repeating themselves.
Yes; every infinitely long number has to start repeating itself sometime.
No; every periodic number is rational, but pi is irrational.

Keep only the '0' and the '1' in the decimal expansion.
It is impossible because pi > 2.
Replace each digit of pi in base 10 with a 0 if it is divisible by 2 and with and 1 if it is not.
Successively multiply pi by 2 and put a '1' when it is greater than 1 and a '0' when it is smaller than 1. Repeat this step after having kept only the fractional part of the result.
Divide pi in base 10 by 5.

el numero bueno
die Ludolphsche Zahl
Gesundheit
die Eulersche Zahl
Drei

Like any normal person, pi has two legs.
Blocks of digits of increasing size have a limit frequency of 1/10 for each of the digits (0 to 9).
Pi squared is a rational number.
People who like pi are normal.
The natural logarithm of pi taken to the tenth power is an integer.

J. Robert Oppenheimer
Kip Thorne
Scott Adams
Elias Bröms
Edmund Landau