Is Marriage Valid without Mahr?
Question

When the marriage contract was done, all the conditions were met of having two witnesses and the wali (guardian), but when the marriage contract was completed, the following happened: My hand was put in the hand of the bride’s guardian, but he read the wording of the marriage contract from a piece of paper, namely “Zawwajtuka… (I give to you in marriage…)”, And he mentioned her name but he did not mention the Mahr. I replied to him with the word “Qabiltu (I accept)”, but after that I agreed with the bride on a very small amount of money. Is what happened valid and is the marriage contract valid or not?
Praise be to Allah.Is marriage valid without Mahr (dowry)?
If the marriage contract was done without any mention of the Mahr , the marriage contract is valid and the wife is entitled to a Mahr like that of her peers.
Ibn Qudamah (may Allah have mercy on him) said in Al-Mughni (7/182): 
“Marriage is valid without stating the dowry according to the opinion of most of the scholars. That is indicated by the verse in which Allah, may He be Exalted, says (interpretation of the meaning): “There is no sin on you, if you divorce women while yet you have not touched (had sexual relation with) them, nor appointed unto them their Mahr (bridal money given by the husband to his wife at the time of marriage)” [Al-Baqarah 2:236]. 
It was narrated that Ibn Mas`ud (may Allah be pleased with him) was asked about a man who married a woman but did not state what her dowry would be (did not “appoint unto her a Mahr”), and he did not consummate the marriage with her before he died. Ibn Mas‘ood said: She is entitled to a dowry like that of her peers, without exaggeration or falling short, she has to observe the ‘iddah and she is entitled to inheritance. Ma`qil ibn Sinan Al-Ashja`i stood up and said: The Messenger of Allah (blessings and peace of Allah be upon him) issued a verdict concerning Birwa‘ bint Washiq, one of our womenfolk, that was similar to your verdict.” (Narrated by Abu Dawud and At-Tirmidhi, he said: this is an authentic Hadith.” 
Types of marriage without stating the Mahr 
Marriage without stating the Mahr is of two types. 

The first is that in which the Mahr is not mentioned at all, and the man gives his daughter in marriage without any Mahr, so he says: I give you my daughter in marriage, and the suitor says: I accept – without mentioning any Mahr, as happened in your case.
The second type is that in which the Mahr is mentioned without specifying its amount, such as if the suitor says to the guardian: I will give you what you want of the Mahr, or the guardian says to the suitor: Give whatever you see fit, and so on.

The wife is to be given a Mahr like that of her peers in both cases.
Who decides the Mahr of a woman’s peers?
The Mahr of her peers is to be defined by the judge, so as to avoid conflict. But if they agree on something without referring to the judge, there is nothing wrong with that, because they have the right to do so.
It says in Zad Al-Mustaqni`: “It is valid to do the marriage contract without mentioning the Mahr or mentioning it without specifying it. The wife is entitled to a Mahr like that of her peers by virtue of the marriage contract, and the amount is to be specified by the judge. If they agree upon something before that, that is permissible.” 
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: “The words “If they agree upon something before that, that is permissible” mean: if they agree on it without referring to the judge, they have the right to do that. In other words, there is nothing wrong with that. So if they say: Why should we go to the qadi? Let us agree on something between ourselves, and the husband offers a Mahr of one thousand, and she asks for two thousand, and some people intervene and suggest one thousand five hundred, and so on, there is nothing wrong with that, because they have the right to any agreement they reach.” (Ash-Sharh Al-Mumti`, 12/315)
Thus you will see that the marriage contract is valid and that the Mahr on which you have agreed is also valid, if the wife is mature and of sound mind.
And Allah knows best.