1. I don’t know well about IT industry. But in other engineering fields, it is not easy for foreigners to get in the industries because there are many American students who want to get jobs. Also, companies need to pay fees when they support H1 visa for their employees. If their employees fail to get H1 visa, companies will lose money and time. That is why American companies don’t prefer to hire foreigners. You should aware that Americans don’t like to make things complicated.
2. That happens often. Don’t relate Job offer and H1 visa.
3. Definitely. You should not complain about this. It is the same with companies in Korea. Do Korean companies prefer to hire foreigners whose Korean is not fluent or cannot speak English? Communication skill is the most important skill required for job applicants in the U.S. Personally, I don’t like to talk to Indian and Chinese because it is stressful to understand their English. It is the same with Americans.
4. At least, there should be no grammatical errors in your written and spoken English. Also, it depends on each company and organization. Some engineering companies don’t prefer to hire foreigners. That is why their HR do video and phone interviews before inviting. There are no jobs don’t require English proficiency. Some Koreans ignore this simple truth.
You can try to study in the U.S. and try to get a job. But it is wholly your choice and your responsibility. That’s all.