Applying cream on the face does not break wudu nor does it break the fast.

Tampons are not haram in Islam. There are hadiths which indicate that it is permissible to use cotton to stop the flow of blood. For more, see the detailed answer.

It is permissible in Islam for women to go out during the 40 days of nifas to any place she wants, so long as she fulfils the Shar’i conditions (i.e., hijab etc.)

Everything that comes out of a woman is impure apart from the maniy. Every other substance that comes out of the two passages is impure and breaks wudu.

If a woman feels that some fluid has come out of her vagina, even if it is only a little, then she has to do ghusl, because of the report to that effect.