Learn English – Is making of ‘right doing’ into ‘rightdoing’ acceptable in a formal speech/writing

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?

Yes, the example sentence you provide could be more formal and more specific (replacing "get" with "access" or "obtain" or "purchase" depending on which meaning is appropriate).

The answer to your question is, to some degree, a matter of style and opinion. "Get" is generally informal, but an absolute prohibition on the word "get" is extreme. For an example of use in a formal setting, here is a quote from a U.S. Supreme Court case (Rucho v. Common Cause): "Free and fair and periodic elections are key to that vision. The people get to choose their representatives."

Despite that example, it probably is a good idea to avoid "get" in formal writing. Beginning (and even experienced) writers often use informal, vague verbs instead of more specific and appropriate choices, and the professor's prohibition on "get" is likely designed to encourage students to think more carefully about their writing. In most cases, "get" can easily be replaced with a more formal option.