My second question is:
Is it permissible for a Muslim woman to look at women at the beach who are wearing bathing suits which show some of what is between the navel and knee and only cover a little bit?.
It is not permissible for a woman to wear pants even if that is in front of other women. See question no. 5066.
It is not permissible for a woman to wear bathing suits and to appear in that in front of people, whether men or women. Whoever does that has done something that Allaah has forbidden and thus deserves His punishment and curse.
Muslim (2128) narrated that Abu Hurayrah said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “There are two types of the people of Hell whom I have not seen…” one of whom was, “women who are clothed yet naked…” According to Ahmad (7043) he said: “Curse them, for they are cursed.” Classed as hasan by al-Albaani in Saheeh al-Targheeb (2043).
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said:
I think that the Muslims should not run after these fashions and styles of clothes that come to us from here and there. Many of them, such as the short and very tight clothes, or light clothes, are incompatible with Islamic dress which involves the woman being completely covered. That includes pants, because they show the size of the woman’s legs, stomach and waist, etc. So wearing them comes under the same category as that mention in the saheeh hadeeth, “Two types of the people of Hell… women who are clothed yet naked.”
Majallat al-Da’wah, 1/1476
The woman who does that should be rebuked and reminded of the fearful punishment of Allaah, and she should be called to repent.
It is not permissible to look at a woman when she is wearing these “naked” clothes, because Muslim (338) narrated from Abu Sa’eed al-Khudri that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “No man should look at the ‘awrah of another man, and no woman should look at the ‘awrah of another woman.”
Al-Nawawi (may Allaah have mercy on him) said:
This shows that it is haraam for a man to look at the ‘awrah of another man and for a woman to look at the ‘awrah of another woman. There is no scholarly dispute on this point. Similarly it is haraam for a man to look at the ‘awrah of a woman and for a woman to look at the ‘awrah of a man, according to scholarly consensus.”
The prohibition on looking at a woman when she is in this state does not apply to the husband, because each spouse may look at the ‘awrah of the other, because Allaah says (interpretation of the meaning):
“And those who guard their chastity (i.e. private parts, from illegal sexual acts)
Except from their wives or (the slaves) that their right hands possess, * for then, they are free from blame”
And Allaah knows best.