1. He dreamed a strange dream.

2. He had a strange dream.
3. He got a strange dream.
4. He dreamed strangely.
5. He dreamt a strange dream.

(Are they all the same and acceptable?)

6. There are three rice cakes in the paper bag.

7. There are three pieces of rice cake in the paper bag.

(Which one is correct? How do we count 'rice cake'? Is rice cake used as a countable noun or an uncountable noun?)

The first two are the best. Numbers 3, 4, and 5 are not commonly used.

Both 6 and 7 sound right to me.

But I'm sending your post to a bilingual Korean-American for her opinion.

#'s 1 and 2 are correct usages.

One does not "get" a dream, and I have never heard of anyone "dreaming strangely". "dreamt" is generally used an a poetic context.

If you can have more than one rice cake, then it is countable. I have seen a number of them on a table.
#6 is correct. I don't know if one would want to break or cut a rice cake into 3 pieces .
Number 6 is correct and unless you can have pieces of rice cake, then I would say that # 7 is not.

1. He dreamed a strange dream.

2. He had a strange dream.
3. He got a strange dream.
4. He dreamed strangely.
5. He dreamt a strange dream.

Regarding the first set of sentences, options 1, 2, and 5 are all acceptable and convey the same meaning. Options 3 and 4, on the other hand, are not commonly used and may sound unnatural or confusing.

In the second set of sentences:

6. There are three rice cakes in the paper bag.
7. There are three pieces of rice cake in the paper bag.

Both sentences are correct, but they convey slightly different meanings. "Rice cakes" is used as a countable noun in option 6, indicating that there are three separate individual rice cakes in the bag. On the other hand, "rice cake" is used as an uncountable noun in option 7, referring to the general concept of rice cake, and it implies that there are three pieces or portions of rice cake in the bag.

The choice between countable and uncountable usage depends on the context and how you want to specify the quantity of rice cake.