1. One noun phrase is :
The conviction of and subsequent 25-year sentence given to Bernie Ebbers.
① The noun phrase is a singular noun or plural noun?
② What is the meaning of such noun phrase?
1.1. It's plural. The sentence might continue "The conviction of and subsequent 25-year sentence given to Bernie Ebbers are two subjects which need to be discussed".
1.2. What is it that you don't understand?
2. I thought him to be an excellent choice = correct
I thought him as an excellent choice. = not correct
I thought that he was an excellent choice. = correct
Are these three sentences correct? The second one is not correct
Do they have the same meaning? Yes, the first and third ones do.
3. I hope to arrive at the conclusion that….
if it is changed into a noun phrase, It is :
My hope of arriving at the conclusion that….
Is that correct?
It's not a correct paraphrase of the first phrase.
4. ① Has she already eaten her dinner?
② Has she eaten her dinner already?
What is THE difference between these two SENTENCES?
The meaning is basically the same, but the second one puts more emphasis on the word 'already'. While the first question is reasonably neutral, the second might suggest surprise or annoyance.
5. ① early examples of his work.
② examples of his early work.
What is the difference between these two phrases?
I don't think there is a difference.