A wife giving up her right to maintenance; and is the first wife’s approval needed before one can marry a second wife?

Maintenance
is one of the rights of the wife which is an obligation upon her husband.
Allaah says (interpretation of the meaning): 

“Men
are the protectors and maintainers of women, because Allaah has made
one of them to excel the other, and because they spend (to support them)
from their means.”

[al-Nisaa’
4:34]

If the
woman foregoes this right, to which she is entitled – which is her maintenance–
then it is no longer obligatory upon her husband. 

Ibn
Qudaamah said: If she agrees to forego some part of her share (of her
husband’s time) or her maintenance, or all of that, this is permissible.
(al-Mughni, vol. 7, p. 244). 

With
regard to the permission and approval of the first wife for a plural
marriage, this is not a condition and the husband does not have to seek
the permission of his first wife to marry a second. But it is prescribed
for him to be kind to her and to spend money and to say kind words so
as to calm her down and reduce her jealousy. The Standing Committee
was asked about the first wife’s approval for one who wants to marry
another wife. Their response was: 

It is not obligatory for the husband,
if he wants to take a second wife, to have the approval of the first
wife, but it is the matter of good manners and kind treatment that he
should speak to her kindly in such a way as to reduce the feelings of
hurt which are natural in women in such cases.  That is by smiling
at her, showing that he is happy to see her, being kind, speaking nicely
and by spending money on her if necessary. 

See
Fataawa Islamiyyah, vol. 3, p. 204