grammar - When the agent takes を in the causative form

I've seen a few sets of terminology when referring to the causative form, so for the basic case, I will use the following: instigator が agent に 〇〇 を ｖ－させる。

In its most basic, text-book form, we have sentences such as:

子供にお弁当を買わせます。
後輩にビールを飲ませます。

Additionally, most textbooks mention something along the lines of [intransitive verbs or verbs that do not call for を] have an agent marked with を。(sorry for the ad-hoc bracketing, but it was hard to parse beforehand)

先生が私をトイレに行かせました。
その人が私をそこに座らせました。

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1. 
   

   If I use 行く with another verb as its purpose, is を available to mark the agent? It seems like this should be the case since お弁当を should be connected to 行く。
   
   Compare:

   
   

   
   

   [a] 子供にお弁当を買いに行かせます。
   [b] 子供をお弁当を買いに行かせます。

   
   

   
   


2. 
   

   With intransitive verbs, must I use を to mark the agent?
   Compare:

   
   

   
   
   

   [a]その人は私をそこに座らせました。
   [b]その人は私にそこに座らせました。

   
   

   
   


3. 
   

   If I leave off the object of a transitive verb due to ellipses, may I mark the agent with を? (This seems strange, but I figured I'd ask.)
   Compare:

   
   

   
   

   [a]子供に買わせました。
   [b]子供を買わせました。

   
   
   

   
   


4. 
   

   If I use a transitive verb, but use を to mark something that is moved through or done with effort, may I still mark the agent with を?
   Compare:

   
   

   
   

   [a]子供に道を行かせます。
   [b]子供を道を行かせます。
   [c]彼に私のことを分からせます。
   [d]彼を私のことを分からせます。

   
   
   

   
   


5. 
   

   I've also heard mention that some speakers occasionally use を to mark the agent with intransitive verbs without any further details. Is this something that a seemingly random group of people does? Is it due to dialectal variation? Is there a pattern to when it can be done? Is there a difference in nuance?

   
   

   In the cases where I can choose between marking the agent with を or に, is there any difference in nuance?
   In a fairly old grammar, I've read that using に may soften the statement a little.

   
   

For each question with example sentences, I'm primarily concerned with a few things:

1. Is this permissible? (would it sound incorrect in conversation look incorrect in writing)


2. What would a native speaker usually do?

Of course I also welcome any information about dialectal variation, language change, etc!