Learn Hardcore Japanese: sumaho de douga wo miruno ha benri desu. - Watching videos on a smartphone is convenient.

In this sentence, で marks the means or instrument you use to do something. So スマホで means “with a smartphone” or “on your smartphone” (i.e., using a smartphone).

What is the role of を in 動画を?

The particle を marks the direct object of a transitive verb. Here 動画 (video) is what you are watching, so 動画を indicates “video” is the object of 見る (to watch).”

Why is there の after 見る? Can't we drop it and just say スマホで動画を見るは便利です?

The の here is a nominalizer: it turns the verb phrase スマホで動画を見る into a noun-like phrase. You need it because you can’t attach the topic marker は directly to a verb; you must first nominalize the clause. Without の, the sentence would be ungrammatical.

What’s the difference between using の and こと for nominalization? Could I say スマホで動画を見ることは便利です?

Both の and こと can nominalize verbs. Generally, の feels more casual and personal, while こと is slightly more formal or abstract. Yes, you could say スマホで動画を見ることは便利です, but it sounds more formal or written than 見るのは便利です.

Why is は placed after 見るの instead of after スマホ or 動画?

The topic of the sentence is the entire activity “watching videos on a smartphone,” not just “smartphone” or “video.” To mark this whole action as the topic, you nominalize it with の and then attach は. If you put は after スマホ, you’d change the focus to the smartphone itself.

The sentence ends with 便利です. Could I say 便利だ or drop です entirely?

Since 便利 is a な-adjective, you can use です (polite) or だ (plain):

Polite: 便利です
Plain: 便利だ
In casual speech, you might even hear 便利 without だ:
スマホで動画を見るのは便利.

Why is 動画を placed before 見る? Could I say 見る動画をスマホで?

Japanese follows a Subject-Object-Verb (SOV) order, so the object 動画を comes before the verb 見る. Saying 見る動画をスマホで is ungrammatical in this context. (However, you can form a relative clause like スマホで見る動画は…, which changes the meaning to “the videos that you watch on a smartphone.”)