Learn Icelandic: Viðskiptin á netinu ganga mjög vel. - Online business is going very well.

The Icelandic noun viðskipti (business, trade, or transactions) is a plural word. Even when referring to the abstract concept of "business" in a general sense, Icelandic requires the plural form. Because the subject is plural, the verb ganga must also be in its plural form.

Would it be correct to use fyrirtækið instead of viðskiptin in this context?

It would be grammatically correct, but it means something slightly different. Viðskiptin refers to the actual commerce, trade, or sales taking place. Fyrirtækið means "the company" or "the enterprise" as a specific legal organization rather than the general act of doing business.

I know ganga means "to walk." How does that translate to "is going" here?

While ganga does literally mean "to walk," it is widely used in Icelandic to describe how things are progressing, functioning, or turning out. Saying that something gengur vel (or plural ganga vel) is the standard metaphorical way to express that it is "going well" or succeeding.

Why does á netinu trigger the dative case for net?

The preposition á governs the dative case when describing a static location or a state of being (where something is happening). Since the business is currently taking place "on the internet," rather than moving toward it, net (with the definite article attached) takes the dative form netinu.