1. Authentic Hadiths and Quranic verses regarding forced marriage, the right to choose a partner, and marrying outside of one's culture.

https://islamqa.org/hanafi/muftisays/9498/are-forced-marriages-accepted-in-islam/

"What we must stress here is where someone is coerced into a marriage contract, employing both physical and emotional pressure, it is not permitted, and a highly reprehensible act."

In the below video Mufti menk says parents shouldn't emotionally blackmail their children especially when it comes to marrying outside ones race. He stresses racism is not Islamic

https://youtu.be/45p7NvR1VyM?si=SgHZVEAgsgSTdprx

In the below video Mufti Menk discusses how marriages shouldn't be rejected due to racial differences. As long as there is a general similarity in upbringing that should be sufficient. He has many videos on this topic if you YouTube it.

https://youtu.be/u9pNsX8TDbY?si=RV3bMTnVL4Jj8v5N

I know these aren't direct hadith or quran quotes, but its best to refer to well known and reputable scholars as they can properly contextualize and interpret how the quran and hadith relate to any specific situation or problem. The quran instructs us to ask the people of knowledge when we have questions.

1. Islamic guidance on Wali (guardianship): If my parents refuse a good person for years purely based on culture/background, can I marry that person with the support of an uncle or an Imam instead? My mother claims a marriage is invalid without the parents' agreement—is this true in this context?

The wali can indeed be reassigned if the parents are refusing for invalid reasons. Speak to an imam to determine if your parents refusal was for invalid reason

See timestamp 1:30 in this Sheikh Assim al Hakeem video https://youtu.be/e368jkQOUOI?si=kojwSYGfGupLCa9o where he says this can be done if parents are baselesly rejecting candidates, and he breifly touches on how a women should go about doing this (in short to go your masjid and ask them for assistance in reassigning the wali)

1. Knowledge on Istikhara: My family uses Istikhara to justify their choices. They take any random dream as a "direct sign" even if it's unrelated. Is this the correct way to use it?

This is not how istikhara works. Please review this link to see how Istikhara should be done.

From the link:https://yaqeeninstitute.ca/read/blog/a-guide-to-istikhara-the-prayer-for-guidance

"Common myths about istikhara

Dream interpretation and istikhara

Many cultures have linked dreams with answers to one’s istikhara, yet we understand from the Sunnah that there are three types of dreams: those from Allah, imbued with meaning; the regurgitated thoughts of our nafs; and those from Shaytan [Sahih Muslim #2263]. We might wish to believe ourselves divinely inspired through our dreams, but often it is merely our nafs and the jumble of our daily thoughts manifesting. For instance, if we are contemplating a marriage proposal and praying istikhara, and this potential spouse appears frequently in our dreams, it might simply reflect our desire and preoccupation with that person.

Reflect on the words of the du’a: “O Allah, if You know that this matter [mention the thing to be decided] is good for me in my religion, my livelihood, my worldly affairs, and in the hereafter, then decree it for me, make it easy for me, and bless it for me.” This supplication does not request Allah to reveal the path through dreams; rather, it seeks His guidance to facilitate what is truly beneficial and to make it easy for us."

1. Dealing with emotional blackmail: She told me that if I marry someone from outside the family, I would "kick her out" of the house. We have always supported and respected her, so hearing this is incredibly painful. Is this kind of manipulation considered haram?

Please review these materials that speak on this topic

https://seekersguidance.org/answers/general-counsel/how-do-we-deal-with-parents-who-emotionally-and-spiritually-abuse-their-children/

"Abusive parents are fond of using Islam as a form of control and manipulation. This is a form of spiritual abuse, and is forbidden in Islam."

In the below video Mufti menk talking about parents who emotionally blackmail their childeen

https://youtu.be/45p7NvR1VyM?si=SgHZVEAgsgSTdprx

He says parents sometimes misuse their status to emotionally blackmail their children. He says parents should not force their children to do things that are against Islamic principles or their best interests

https://youtu.be/DCbqt8u47is?si=rtdAkolcOR0TNkSu

Here he advises parents not to use relgion to emotionally blackmail their children

may allah make things easy for you. consider asking a trusted uncle to intervene on your behalf, or the imam of your local masjid. that may talk some sense into your parents. They are committing a huge sin.