I take it that 们 is a plural marker and 我 is first person, right?
Yes, it is.
Yes, but only for titles, occupations and pronouns, other words don't really come in plural form.
Wouldnt it be more correct to add 的 after 我们？
It's nearly the same, 我的will make 姓a noun, and 我姓will make 姓a verb. My surname is... And I'm "surnamed "... Which is more used :)
So if we use 的, 姓 is not a verb anymore, then there is no verb in the sentence and you would need 是? i.e. the sentence with 的 would be?
or can you make a sentence without a verb in Chinese?
shì isn't really a verb, more of a confirmation while bù is the negation, like zài is no verb per se. Thus your sentence indeed does not contain a verb per se. Our ([pro-]noun) surname (noun) is (not really a verb) Wáng (noun).
姓 is a verb in these sentences.
At times 的 is omitted when there is a close association
Wouldn't it make more sense to be "Our last names are Wang."?
I think the sentence is about a family, so it's one shared name. But you could be right if they are from different families (it's a very common name).
no that implies that you have multiple last names
I am right!!!!!
Shouldn't be 我们的 ？