I do not really understand the use of participles in these kind of sentences.
1- We spent the first month just debating what to call ourselves.
2- You had no business reading my private letters.
3- I have a job bussing tables at the coffe shop.
Are all of the sentences above missing out "in"
1'- We spent the first month just in debating what to call ourselves.
2'- You had no business in reading my private letter
3'- I have a job in bussing tables at the coffe shop.
4- I work at the coffee shop bussing tables.
I think the latter one okay to me(4). My interperation is something like that for the use of participle:
Bussing tables is part of working at the coffe shop.". In the process of working at the coffe shop, I am bussing the tables.
But I can't understand the use of the participle in the other sentences.