Learn Russian: Кто против?

No, though they look similar and both take the Genitive case when followed by a noun. Напротив means 'opposite' or 'across from' in a physical sense. Против means 'against' in an abstract sense, like opposing an idea or proposal, which is how it is used here.

Where is the word for 'it' in the Russian sentence?

It is completely omitted! In Russian, when the context is clear, you can use против on its own to mean 'against it' or 'opposed'. You do not need to add a pronoun like этого unless you really want to emphasize what you are against.

Why is there no verb for 'is' in this sentence?

Just as a quick refresher, the present tense of the verb 'to be' is almost always left out in Russian. So, Кто против? literally translates to 'Who [is] against?'

If I wanted to specify what we are against, what case would I use?

You would use the Genitive case, just like with the prepositions taught in this lesson. For example, 'Who is against this plan?' would be Кто против этого плана?