1 Question: Is it permissible for a Muslim man to go to a mixed swimming pool with the knowledge that the women there swimming suits form and would not listen to any admonishing?
Answer: Although looking without bad thoughts or lustful intentions at the women who are indecently dressed (and who would not listen to you if you wish to admonish them) is allowed, yet based on obligatory precaution, going to such places is absolutely forbidden.
2 Question: Is looking at one's mother's face Ebadah (a kind of worhsip)?
Answer: Yes, as stated in a tradition, if you look at her face out of kindness and respect when she is old and emaciated, it is a kind of worship.
3 Question: Can I look at a girl whom I intend to marry in the future? I mean can I look at her body in order to see if she is suitable for me or not? There is a probabality that if I like her, I mighy marry her.
Answer: If there is a probability that you will marry her, you can look at her only once.