Re: essential adjectival or adverbial phrase?

Hi. Would you say the phrase that begins with the participle "running" is an adjectival phrase describing the oil? Also, would you say the phrase that comes with(?) it is an essential element and had it not had for the prepositional phrase "in a bottle," a comma wouldn't have been needed?

It is like oil in a bottle, running down the top.

I think no comma is needed after the word "day" for this one. Unlike the one above, I think the underlined part is an adverbial phrase.

He spent the rest of the day studying for the upcoming test.

But if there happens to be a (another?) prepositional phrase like "in the room," then I feel a comma is needed after the word "room" eventhough the phrase "studying for the upcoming test" is still essential to the overall sentence.

He spent the rest of the day in the room, studying for the upcoming test.