1. Is it welcoming to people who are not of Indian descent? Particularly, to people of African descent? (I'm an African American female).
Your ethnicity does not matter. I have met African Indians and Caucasian Indians. You can reach the highest posts of Hinduism irrespective of which ethnicity you are. Swami Kriyananda, a disciple of Swami Yogananda, is a Caucasian male.
There are some very small sub-sects in India that do not allow foreigners, but they are rare.
2. How does the religion treat "liberal" ideals such as women's rights and equality, and gay rights?
For the most part they are very liberal. The woman has a very high position in Hinduism because the woman is considered to be the divine mother. Most Hindus worship the divine mother as mother nature. There are several examples in Hindu history of very powerful women, such as Sita, Drupadi, Gargi, Rani lakshmi bhai. About 30 of the authors of the Vedas are women.
In the ancient period Hindu women had the most rights. In the Arthshastra, written by Kautaliya the professor of politics and economics at Taxshilla university in ancient India, womens rights is an important part. Her rights include rights to property, rights to divorce, rights to alimony, rights to inheritance, rights to remarriage and rights to work.
Gay people in Hinduism are largely a neutral issue. It is more of a live and let live philosophy. There are important gay historical personalities which are respected, like Shikandi from the Mahabharata. In Hindu art in some temples, homoerotic symbolism is used. In modern day, some Hindus think homosexuality is a disorder, but still tolerate gay people. Baba Ramdev, a famous guru of Yoga and Hinduism in India today, believes homosexuality is a disorder and it can be treated using Yoga.
3. I understand that the cow is held in high regard...what is the reason for this? And do Hindus generally eat any meat at all?
The cow is the most important animal in Hindu society because it was used so much. It is given high connotations like mother, knowledge, light, goodness. It is considered in the mode of goodness. Thus it enjoys a lot of respect.
Hindus prefer vegetarianism. Of course you do find many Hindus who eat meat. But vegetarian is considered more good, noble and spiritual.
4. Does Hinduism have "sacred texts" or are teachings varied according to the writings of individual gurus?
The Vedas and the Upanishads are the core of Hinduism. In fact when we use the word "Vedas" we are referring to both the Vedas and the Upanishads. However, these texts are written in very archaic language and difficult to translate(translations of the Vedas are especially controversial) This is why Hindus prefer the Bhagvad Gita, which contains the essential teachings of the Vedas.
Most Hindus, however do not read scriptures, and learn Hinduism through the stories of the Mahabharata and Ramayana. Every Hindu knows these epics very well.
The distinction between Hindus who read the Vedas, Upanishads and Gita and the Hindus who know it from the epics is significant. You will get a more technical, philosophical and accurate understanding of Hinduism from the former. The others, will only have a rudimentary understanding.
5. Do Hindus of different sects look at other Hindus outside of their sect as not being a "true" Hindu?
Nope, even though Hinduism has many sects and sect prefer to worship one Hindu god or goddess more than the other, they tend to worship them all. A vaishnavite who worship Vishnu, will also worship Shiva and the divine mother too.
6. Have any of you become Hindu from another religion or a lack thereof? If so, what brought you to Hinduism?
I was born Sikh, then later became atheist. What bought me to Hinduism was science. I realised how all Hindu teachings were backed up by science and how so many famous scientists supported it. This is why it sometimes called the scientific religion.