When should I write わたし instead of 私?
I cannot imagine any particular case that Japanese people have to write わたし instead of 私. To a beginner of the Japanese learning, I would like to advise to use 私 instead of わたし in any case.
As a Japanese writer, however, I often avoid using 私 in my writing, because I think it better to use hiragana when using the words originated in Japan, not in China. So my ideal is to write original Japanese words in hiragana and to use Chinese characters in writing many words originated in China. This is only my rule or ideal but in practice I have to use 私 instead of わた(く)し not to make my sentence ambiguous or difficult to read because of a long sequence of hiragana.