Keep dreaming is a staid, somewhat dry phrase. It can be used in many contexts, formal and informal. In this usage, dream can have several meanings.
I am not finished with my REM tests; please keep dreaming.
Keep dreaming, and you will never face reality.
Keep on + ing verb = Keep continuing/trying to + verb.
Keep on dreaming = Keep continuing/trying to dream.
Dream here means hope. It does not refer to having dreams while asleep.
Keep on dreaming is an idiomatic usage, usually used in informal language. The on in the phrase provides the idiomatic/informal nuance of continuing to, usually indicating encouragement, much as it does in keep on trucking.
I feel like giving up on my lifelong dream, but my brother says I should keep on dreaming.
Note, Keep on dreaming and keep on trucking do not have the same meaning, but the on in both phrases serves the same function, namely to stress the aspect of continued trying or continued attempting to try.
We also have the phrase keep on keeping on, which is informal encouragement to continue battling through whatever obstacles one faces in life.
Life is so hard, but I have to keep on keeping on.
Prepositions don't have to be part of a phrasal verb, in fact I would say most aren't. In this case, none of the prepositions have any special relation to the verb. They're all literal descriptors of the positions the subject goes through during the action.
Try to break up the sentence into the smallest chunks that make sense. Here: He fell. Yeah, that makes sense, that's true. Okay, where did he fall? Into the pool. What did he fall off of? He fell off the ledge. So now, put it together.
He fell off the ledge and into the pool.
You can leave out the "and" here, but it's still there for grammatical purposes. You can tell if you use three prepositions:
He fell off the ledge, through the air, and into the pool.
You can't leave out the "and" here, there's no way to use three prepositions without the conjunction. That means that there's no way to do it with two, either, and the "and" is still there, it's just not spoken.
Right and straight are both intensifiers, and don't really make sense to me here. There's not exactly an indirect way to fall off a ledge and into a pool.
I hope this helps.
Edit: A note to help distinguish between phrasal verbs and normal prepositional adverb phrases: phrasal verbs don't accept objects of the preposition, and they don't pair with prepositions in conjunction phrases.
The roof fell in. good
The roof fell in the house. not good
The roof fell in and onto the ground. not good
The roof fell in onto the ground. good
Does that help you see the difference a little better?
Best Answer
is often gets used to spur someone or something to start.
In your case you are continuing to do something
are both appropriate.