Demanding dowry
The Shariah has prohibited a believer to beg from somebody without a stringent, pressing need. There are warnings in the Hadith about this:
Translation of Hadith: There is a very lengthy Hadith narrated on the authority of Hadhrat Habshi Bin Janadah As Saluli in which the Holy Prophet (Sallallahu alaihi wa sallam) said: Begging is not permissible for some who is wealthy and someone with a sound body, excepting for someone who is very poor and someone in a very great need. If a person begs to increase wealth, then in Qiyamah, that begging will be on his face in the form of scratches and it will come in the form of an ember, from which that person will eat. Whoever wants to can decrease or increase this punishment for himself.
(Jame' Tirmidhi, Kitab Uz Zakaah, Vol. 1, Pg No. 141, Hadith No: 590)
However, without any demand of any kind, exchanging gifts willingly is allowed. Islam has declared exchange of gifts to be a means of maintaining and increasing love, as the Holy Prophet (Sallallahu alaihi wa sallam) said in Kanz Ul Ummal, Hadith No: 15057). Thus, giving a gift on the occasion of marriage is permissible.
Un-Islamic customs in marriage
On the occasion of marriage or other happy occasions, there is no problem if a function is held within the limits prescribed by the Shariah, but roaming before a non-Mahram without any Hijab, making the sister-in-law hold one's hand and/or applying Mehndi (henna) to the fingers is all impermissible.
The Holy Prophet (Sallallahu alaihi wa sallam) said:
Translation of Hadith: In Qiyamah, molten lead will be poured in the eyes of the one who looks at the beauty of a woman with desire. (Bidayah wan Nihayah, Kitab Ul Karahiyya, Vol. 4, Pg No. 458)
Touching a Non-Mahram is strictly impermissible. There is a Hadith:
Translation of Hadith: In Qiyamah, a burning ember will be placed on the hand of the one who touches a Non-Mahram woman. (Bidayah wan Nihayah, Kitabul Karahiyya, Vol. 4, Pg No. 459)
Therefore, the customs which are against the Shariah in Sanchak need to be dropped.
Does the daughter not receive a share in the inheritance because of marriage expenses?
If the parents are distributing their property in their life itself, then they should be just and give an equal share to all children. If a son/daughter is financially weak, they may give an extra share as well.
However, if the property is distributed after their death, then the inheritance will be distributed as per the injunctions given in the Holy Quran and the Hadith only.
Valima with bride’s money
In the light of Holy Islamic Shariah, putting the weight of some function or celebration on some one else is improper. One conducting a modest function according to his means and convenience with a cheerful heart is far better than a grand celebration without the same.
However, since the Valima is a Sunnah of our Holy Prophet (Sallallaahu alaihi wa sallam), the groom can invite his near and dear ones in it as per his convenience. From the initial period of Islam onwards, arrangement of Valima was done by the groom itself and no help was sought from the bride's family, but if the bride's family members wish to share the expenses of Valima without any demand or coercion; then there's no objection to it according to Shariah. Nevertheless, forcing the bride's family to share the expenses of Valima is prohibited, as per the Shariah.