What is the difference between "we" and "wij"?
"Wij" is "we" but said with emphasis, they're otherwise the same word
It's not about saying it with emphasis or not.
In some cases using we is incorrect. When contrasting or highlighting groups.
The correct answer says wij schrijven een boek i thought it shoul be we scrijf een boek? English is not we are writing a book but we write a book?..
Is the F changing to a V unique to Schrijf, or is it a rule for words ending in F?
This happens whenever a word ends on F and the vowel before it is long (usually a diphtong or double vowel).
There's some more information here.
When does one use 'we' and when 'wij'?