The code is now working.
It was wrong all over. I messed up pretty much any part that I could regarding the dynamic memory while trying to fix it before.
I initially didn't care about calling 3 times to strlen becuase it's just homework and a very small program but I guess it's better to get used to do things the right way... I also dropped the copy which I evidently don't understand very well in favour of a simple for loop.
// Add function. The rest is cut.
int word_length = strlen(word);
temp[i] = new char[word_length + 1]; // Added +1 here.
temp[i][word_length] = '\0'; /* This was correct after all.
the word_length index is the correct ending.*/
for (int j = 0; j < word_length; j++) // copy replaced by for loop.
temp[i][j] = word[j];
// cut
}
void Delete_Word(char**& dictionary, int& dictionary_size, char* word)
{
delete[] Search_For_Word(dictionary, dictionary_size, word);
// There was a -1 mistake here I made in order to try and fix the thing earlier.
// No need for more, it works perfectly now.