1. What does this imply for the Zeeman splitting of singlet states?
Recall that
What does this imply for the Zeeman splitting of singlet states?
Nothing.
The term splits asymmetrically around the unperturbed term.
The term does not split.
The MJ sub-levels of all singlet terms split by the same amount.

2. What does this imply for the Zeeman splitting of singlet states?
Recall that
What does this imply for the Zeeman splitting of singlet states?
Nothing.
The term splits asymmetrically around the unperturbed term.
The term does not split.
The MJ sub-levels of all singlet terms split by the same amount. ... because gJ = gL = 1 for singlet states. Since 
for all singlet states.

3. Consider the transition 1D2  1P1 in Cd at 643.8 nm. Into how many
different spectral components does the transition split in a weak
external magnetic field? 2 3 4 5 6

4. Consider the transition 1D2  1P1 in Cd at 643.8 nm. Into how many
different spectral components does the transition split in a weak
external magnetic field? 2 3 4 5 6
so we only get 3 different transition energies, one each for
mJ = 0 and 1