My friend just found out that her cancer is a treatable variety. Is there a Hebrew phrase to thank Hashem for this good news? Baruch Dayan HaEmet I believe is only for news of a death, but thanks for a merciful judgement?
You should really ask a Rav.
In general, there's this Halakha (following quoted from here):
For hearing good news from a reliable source which is good for oneself and for others one should make the Bracha of HaTov VeHaMeitiv. However, for hearing good new which is only good for oneself, one should make Shehecheyanu. (Kitzur Shulchan Aruch 59:1)
Note that after her treatment, she may be obliged to to make Birchat HaGomel (you can read about it here). Please, ask a Rav.
It's common to say Boruch Hashem which sometimes is translated as 'Bless is the Name' or 'Thank Hashem'.