She gets a sticky white discharge before her period and a week afterwards

Firstly: 

This sticky white substance
comes under the same ruling as other secretions, and is subject to further
discussion. 

If it is continuous, then
it comes under the same ruling as urinary incontinence, so you have to do
wudoo’ for each prayer after the time for it begins, and these discharges
will not matter after that, even if that happens during prayer. 

If it is not continuous,
then there is a difference of opinion as to whether it invalidates wudoo’.
The majority of scholars are of the view that it does invalidate wudoo’, but
some of the scholars are of the view that it does not invalidate it, because
there is no evidence to that effect. But to be on the safe side, one should
follow the view of the majority. 

Secondly: 

This discharge is taahir
(pure) according to the most correct view, so there is no need to wash them
off one’s clothes. This is the view of Abu Haneefah and Ahmad, and it is one
of the two views narrated from al-Shaafa’i, and was regarded as correct by
al-Nawawi. 

This view was also favoured
by Shaykh Ibn ‘Uthaymeen. (May Allaah have mercy on them all.) 

He said in al-Sharh
al-Mumti’ (1/329): If these discharges come from the vagina, then they
are taahir (pure), because they are not waste products of food or drink, so
they are not urine. The basic principle is there is no najaasah (impurity)
unless evidence is established to that effect. And if a man has intercourse
with his wife, he does not have to wash his penis or his garment if anything
gets onto them; if it were naajis (impure) then that would imply that maniy
(semen) would become naajis, as he result of being contaminated with it. End
quote.  

See also al-Majmoo’
(1/406); al-Mughni (2/88). 

Thirdly: 

These discharges do not
affect the fast. 

To sum up: you may fast and
pray, and you should do wudoo’ when these discharges come, unless they are
continuous and last all day, in which case you should do wudoo’ for each
obligatory prayer when the time for it begins, and you can pray with this
wudoo’ whatever naafil prayers you wish, until the time for the prayer for
which you did wudoo’ ends. 

And Allaah knows best.