Seneca, sorry, I understand about the too many cooks.
Please feel free to chip in any time. It is very helpful to hear from someone who is working on this textbook. I did not use M. to learn Greek so I am coming to this fresh. All I meant was that Lukas ended up being more confused and I didn’t want him to feel overwhelmed. That said it is helpful to have different points of view. Also I make mistakes and it is helpful to have those picked up.
Establishing the grammatical connection between the circumstantial participle and the main clause would normally be the first step. As M. says “The circumstantial participle may agree with the subject, the direct or indirect object, the object of a preposition, or any other noun or pronoun expressed or implied in the sentence.” I think Lukas found it difficult to work out what the main clause was and how it worked.
The sentences you posted would be good practice for Lukas to see if he understands this aspect of participle use.
It would also be worth looking at the sentences in North and Hillard Greek Prose Composition available via a link here http://discourse.textkit.com/t/the-textkit-book-collection/17987/1 p.122. I think as I have said many times that the problem with M. is that there are not enough exercises nor text to read.