Hello, everyone! I have lots of questions according this sentence. Hope you guys can help me again.

It was the White Rabbit, trotting slowly back again, looking anxiously about, as if he had lost something?

I need to analysis this sentence and write down the form and function of the sentence. Moreover, I need to have the explanation.

First of all, I am not sure of the form of this clause 'Trotting slowly back again.'
-Is back an abverb or preposition? Explain to me pls.
-Is again an abverb here? Explain,pls. ( Is it possbile to have 3 abverbs in a sentence?)
Second, 'looking anxiously about': Is 'about' a preposition? But I don't know how to explain.

Third, is 'as if' a conjunction?

Lastly, I have written some explaination of this sentence, pls give me some comments:

The sentence type is SVCA (or do I need to write SVCAAA?, which one is correct?). It starts with a cleft structure in order to help us focus on 'the White Rabbit'. Here the noun 'Rabbit' is singular and in capital form which defines as a proper noun. The noun phrase 'the White Rabbit' is a subject complement (my tutor told me that it is a new sentence and no need to care about the previous text) which states the subject more clearly.
However, I don't know how to finish the conditional clause (as if he had lost something).

Thank you to all of you!