"There are many trees around my house."
“周围” is a preposition rather than a verb. You might have mistaken it for “包围”. But “包围” is not the best choice here because it is an action usually carried out by people.
Sounds wrong. Syntax is, just about, all there is in Chinese grammar, so it is more fixed than English. Btw a typo in your Chinese: it is 樹 （tree） not 書 （book）。
Place adverbs have to go before the verb, either between the it and the subject or to the very front. The only case where a place can go after the verb is if the verb is something like 在 or 去 which require a place to make sense at all. For these verbs you can think of the place as the object of the verb.
I think zhou1wei2 is a proposition, not a verb. So it's more like 'around' instead of 'surrounds'.