I hope you could answer some of my questions this time

Can you say: I use the Internet to do my homework researches or is it better to say for doing my homework research/for homowork research?

After a little period OR after a short time OR after a while ???

In a first time OR in the beginning he enjoyed being Hyde???

M.L.King had a dream that all human races would have the same rights OR DREAMED THAT oR only wished is possible???
Alternatives to animal testing are analysing statistics OR statistical analyses???

Thank you

Can you say: I use the Internet to do my homework researches or is it better to say for doing my homework research/for homowork research?

I'd say, "I use the Internet to do my homework and research."

After a little period OR after a short time OR after a while ???
It would be good to have a whole sentence. Any of these would do, but it depends on the rest of the sentence. What did you have in mind?

In a first time OR in the beginning he enjoyed being Hyde???
"At first, he enjoyed being Hyde."

M.L.King had a dream that all human races would have the same rights OR DREAMED THAT oR only wished is possible???
I'd say, "M. L. King, Jr., had a dream that all humans would have the same rights."

Alternatives to animal testing are analysing statistics OR statistical analyses???
I'd say, "Alternatives to animal testing are analyzing statistics." (Or you would write "analysing" if you are in England.)

OR -- for that last one:

"Alternatives to animal testing include the analysis of statistics."

Sure, I can help you with your questions!

1. The phrase "I use the Internet to do my homework research" is grammatically correct. However, you can also say "I use the Internet for doing my homework research" or "I use the Internet for homework research." All three options are valid and convey the same meaning.

2. The phrase "after a little period" is not commonly used in English. It would be better to say "after a short time" or "after a while." Both phrases mean the same thing and can be used interchangeably depending on the context.

3. The phrase "in a first time" is not typically used in English. Instead, you can say "at first" or "initially." For example, "At first, he enjoyed being Hyde." This indicates that his enjoyment was temporary or changed over time.

4. The original statement "M.L.King had a dream that all human races would have the same rights" is grammatically correct and accurately captures the idea of Martin Luther King Jr.'s dream. However, you can also say "M.L.King dreamed that all human races would have the same rights" or "M.L.King wished that all human races would have the same rights." These alternative phrasings maintain the same meaning and are equally valid.

5. The phrase "alternatives to animal testing are analyzing statistics" is not grammatically correct. Instead, you can say "alternatives to animal testing include statistical analyses." This conveys the idea that statistical analyses are one of the methods used as alternatives to animal testing.

I hope this clarifies your questions! If you have any more, feel free to ask.