A marriage proposal is an event where one person in a relationship asks for the other's hand in marriage. If accepted, it marks the initiation of engagement, a mutual promise of later marriage. It often has a ritual quality.
If her father is non Muslim and she is a Muslim, then no authority for her non Muslim father on her and she will be able to decide her marriage with suitable believer.
A woman is not required to marry a man just because he wants to marry her. She is also not required to give a reason for refusing. Marriage is optional.
The opposite is also true - that is, a man is not required to marry a woman just because she wants to marry him, and he is also not required to give a reason for refusing.
The idea a woman must give her life over to a man simply because he asks - unless she had a reasonable excuse - would indeed be an astonishing form of male privilege.
Main criteria for marriage in Islam is religious practice and good morals. Financial status is not among the main conditions. In fact the Prophet (SAWA) proposed a marriage between very poor person ( Jowaibir) and a very rich woman (Al-Dhalfaa').
The man should be able to earn livelihood for him and his wife and live with his wife with dignity.
Istikhara is not obligatory in every marriage. It is helpful if you are unable to decide whether the proposal is good or not.
The Istikhara which you did is for your intention, while the Istikhara which the boy did was for his intention. You need to wait till any change in the circumstances takes place, then if you remain unable to decide and you still need an Istikhara, then both should go for one joint Istikhara.
Yes it is permissible for a woman to propose marriage to a suitable man. She can convey her proposal through a trusted person or through any suitable way like a letter or an email etc. Such proposal should be studied very carefully because it is not common among men, and it might be misunderstood or misused if the man is not pious enough. The man should be with high degree of faith, religious practice and manners.
As Muslims, we do not believe in caste, and we rather condemn such an attitude. Our criterion for evaluating someone is piety, as the Quran says. It is unfortunate that some parents still carry such a mentality, and hopefully one day we will all be able to implement our religion in the best way possible.
That being said, you must take into consideration compatibility and overall mindset of who it is you are marrying. There must be a good level of compatibility for you and your future spouse to have a successful marriage. It would be best for an elder or a local scholar to somehow discuss this topic with your parents, if you see this suitor to be appropriate for you to marry.
Do not allow this to escalate, or turn into major problems, and try to deal with it in a calm and wise way.
As for "love marriage", this is an unfamiliar term in Islam. For us, it is either marriage, or not. Love is one thing, and legitimacy of a relationship between two non-mahram people is another.
With prayers for your success.
Although from a shar'i perspective this might not be obligatory, but one is asked it would be haram to lie and not tell the truth.
Also, ethically it is important for both sides to be transparent and clear about everything. Present everything to each other, and it is up to both sides to decide and agree, or disagree.
The problem with concealing such information is should it surface later on, it will become very difficult to contain and could lead to deep issues.
If your question is regarding who the Wali 'Amr is, and a wali amr in this case refers to the Islamic guardian, who is the father, or the father's father, then there are few scenarios:
If the girl is a virgin, and not religiously independent (rasheedah) her wali amr can be a male who her father has appointed in his will. If the father has not appointed anyone in the will, then her wali amr is a Jurist who carries all the required conditions of Ijtihad. The Mujtahid that she selects will be her authority and her guardian. This means that the Mujtahid can approve the marriage, and hence it will be legitimate.
If she is rasheedah, and rasheedah in this Islamic context means a woman who has not been married, but is individually, socially and financially independent and she alone makes her own choices and decisions. In this case, she does not need consent from anyone.
In any of these above cases, it is crucial that family members be involved as well. For example, even though from a shar'i perspective she does not need to seek consent from her mother, or her uncles, or elders, but it is indeed morally and socially very important to do.
And Allah knows best.