Translation:She promised to write me every week.
I think that would be more like "toda a semana" or "a semana inteira."
Toda semana = todas as semanas = every week.
Toda A semana = A semana toda = all week
Cada is indeed "each" (preferrable) and "every" (when each is not good).
But "toda semana" = every week. (And it's better than cada)
"promissed" is definitely incorrect, although it got 6,000,000 hits on Google versus 98,000,000 for "promised". So the Duolingo writer has a lot of company.
Seems to me, from traces in many sentences, that Duolingo writer is Brazilian.
A Brazilian would think "promissed" is better than "promised" if he were in doubt.
The english translation should include write to me, not write me, that is bad english.
I'm not sure that's true, but in any case, "She promised to write me" is very common.
Duo won't let me report that the English sentence is unnatural in this exercise. British English should be "She promised to write to me every week" - "write me" is American. Very annoying.