Learn English – article before the noun before and after “and”

Where "business" is being used in a similar context to "company" or "organisation", and as such is countable, you need to make sure you use an article.

It goes into the business as well. He is running a business.

Or:

He has been running the business since day one.

So both of your phrases above require an article.

However, the term "business" can also be used as a concept, describing trade (see its various definitions). In this case it is an uncountable (conceptual) noun, and so no article is needed.

Business is going well at Blah Blah Blah Inc's Headquarters.

One could say:

The students in Mr Smith's art class were at their easels, looking at the sunset.

In that case, the sunset is the object of scrutiny, and it refers to the entire western sky as it is lit up by the setting sun.

But when it is used to indicate a time of day, the idiom is "before sunset", "after sunset", "at sunset".

EDIT: CopperKettle's examples on the use of "the" with a proper noun are good ones. Here are some others in the same vein; perhaps we can extract the essence from them to show when it is appropriate to use "the" with the proper noun.

I do not know you any longer! What has happened to the gentle Henry Jekyll, the Henry Jekyll with the wry sense of humor and a fondness for good port?

Get up off your ass, Jones, and get back on that horse! Where's the do-or-die Jones, the gung-ho Jones, the let-me-at-them Jones who volunteered for this mission??? I don't like this new sissy Jones who is afraid to ride on a pony just because it's a little skittish.