Sample Mandarin Grammar (Sentences)
UPDATE with answers:

Q0: example of a sample compound sentence

o. 她跳舞, 我歌唱.


Q1: Could someone supply a sample Mandarin Chinese complex sentence here?

a. 那是**我遇见她的**房子. (adjectival clause)
b. 我知道**答案是什么**. (noun clause)


Q2: Could someone supply a sample Mandarin Chinese compound-complex sentence here?

x. 她跳舞, 我知道**_她跳的_是什么舞**.


(this is partly using o and b)

Q3: Have I missed any major Mandarin Chinese sentence types? 

No, I think the three types (simple, compound, complex) are the major ones.
Again, compound-complex / complex-compound is just built on compound and complex.

(note: I am not able to make the characters bold or italic in the above sentences)



I will start with your Q3:

I think simple, compound, and complex are the three types. You can count compound-complex / complex-compound as a fourth, but it's really building on compound and complex.

I am inclined to believe that compound sentence and (some of) complex sentence (*) in English tend to be the same thing in Mandarin.

(*) Adverbial_clause

Compare this example: 

I ate breakfast before I washed the dishes. (A)


to this one:

I ate breakfast, and I washed the dishes. (B)


The distinction between before (adverb) and and (conjunction) is not so big in Mandarin.



The noun clause and adjectival clause are a different story though.

For noun clause (and an answer to your Q1), if we consider this as complex:

I know who said that.


then we have this complex Mandarin sentence:

我知道是谁说的.


(Note that the addition of 是 and the omission of that, which changes the sentence structure quite a bit. Due to that, I don't know if the Chinese sentence should be counted as complex.)

Similarly, when you think of adjectival clause:

That is the house where I met her.

can be translated to:

那是我遇见她的房子.


Probably that is what makes you think that

the sentence types below apply to both English and Mandarin Chinese languages


As a side note, 
I think the classification of simple, compound and complex is more or less based on English, like this one.