Woman showing her eyes

Yes, it is permissible for a woman to show her eyes. That is
so that she will be able to see. But it is not permissible for men to look
at the eyes of a woman. 

Shaykh ‘Abd-Allaah ibn Humayd (may Allaah have mercy on him)
said: 

If the burqa’ [a kind of face veil] covers the entire face,
leaving only the eyes uncovered, there is nothing wrong with that. But if it
does not cover the entire face, rather it covers the mouth and leaves the
rest of the face uncovered, that is not permissible, especially in the
presence of non-mahram men. 

So the entire face must
be covered, but the eyes may be left uncovered so that the woman can see
where she is going, as was said by Ibn Mas’ood, ‘Ubaydah al-Salmaani and
others. And Allaah knows best. 

Fataawa al-Mar’ah al-Muslimah,
1/393, 394. 

And Shaykh Saalih al-Fawzaan (may Allaah preserve him) said: 

There is nothing wrong
with covering the face with the niqaab or burqa’ [kinds of face veil] which
has two openings for the eyes only, because this was known at the time of
the Prophet (peace and blessings of Allaah be upon him), because there
is a need for that. If nothing shows but the eyes, that is acceptable,
especially if that is what women customarily wear in that society. 

Fataawa al-Mar’ah al-Muslimah,
1/399 

But we should note that the majority of women, nowadays, do
not stop at uncovering the eyes only, rather they go beyond that and uncover
part of the forehead and nose, so they go beyond the area that it is
permitted for them to show. Hence some of the scholars – such as Shaykh Ibn
‘Uthaymeen (may Allaah have mercy on him) – forbade wearing the burqa’ and
niqaab, because of the careless attitude on the part of some women.