ousted from hostfamilies house

I live with my host family while studying abroad now.

Today, I came back at 6:30 when I finished.

You said came back and then go back, which would make the meaning confusing. So I assume you mean when you were able to leave you went home?

Few minutes later, my host mother told me "come on, the dinner is ready."

As soon as I ate dinner, my host family said to me "eat quickly, eat quickly "

I couldn't understand the reason why my host mother made me eat so quickly.

Let sounds like you wanted to. Made means you were being forced to.

After 5 minutes, the entry phone rang and the host family's friends were coming in the house.

It's either 'later' or 'after', not both. I'm not too sure what an 'entry phone' is though. Do you mean 'intercom' (インターフォン)?

Then I first realized that she made me eat so quickly so she could eat dinner with her friend .

It made me a little bit angry.

'Made' is past tense of make.

I wanted my host mother let me know earlier, because if I knew that, I could go back and eat earlier so I wouldn't disturb her.

Past tense of 'know' in the middle of the sentence because you would already know by that moment if she told you. The 'so' is because that is caused by knowing.

She continued to say to me "eat earlier, eat earlier."

The more she said to me, the angrier I became.

I got impatient and said to her before her friends "if you want to eat dinner with your friend, why didn't you inform me earlier."

"If you inform me earlier, I could eat dinner earlier"

My host mother looked a little bit angry, and said to me "OK, go upstairs"

After she finished eating dinner, she let me go downstairs.

Was it her that finished eating or you?

I anticipated that something bad would happen.

Past tense

She said to me "Why did you say to me that in front of my friend?"

Question mark to show it was a question. Same as か in Japanese.

I was ashamed.

Is this still her talking? Or you thinking? If she is still talking then you need the quotation marks " around the whole thing.

I don't want to live with you anymore.

I'll take care of you until the contract expires, but after that you have to move to another house.

So I have to move to another house.