Learn Dutch: Het is alsof we in een andere stad rondlopen. - It is as if we are walking around in another city.

The word alsof (as if) is a subordinating conjunction. It introduces a dependent clause, which always pushes the conjugated verb to the very end of that clause.

Since rondlopen is a separable verb (rond + lopen), shouldn't it be split up here?

In a normal main clause, it would split (for example, we lopen rond). But because alsof pushes the verb to the end of the clause, the two parts of the separable verb are forced back together and written as one single word.

Why is it een andere stad with an -e on the adjective, instead of een ander stad?

The word stad is a de-word (de stad). Adjectives placed before de-words almost always get an -e ending. The only time you drop the -e after een is when the noun is a het-word.

Could I translate "It is as if..." using het is net als instead of het is alsof?

Not quite! You use net als (just like) to compare two similar, real things or people. You use alsof (as if) to introduce a hypothetical situation or a non-literal comparison, exactly like in this sentence where you aren't actually in another city.