Ramadhaan & Fasting

Unintentionally inhaling dust while fasting

Q: My question is related to the validity of the fast. 

While doing my Kaffarah, I was cleaning my home and dusting off some shelves on the 58th day out of 60 days. Some dust flew in the air and I inhaled it. I looked the issue up in Maraqi al-Falah and it said in the chapter of that which does not invalidate the fast, "dust or smoke alongside smoke from wood or incense entering one’s throat without one’s doing". 

Here, it is mentioned, that smoke and dust which is inhaled by ones own doing will invalidate the fast. Does the aspect of causing it oneself only apply to smoke or does it apply to dust, too? 

Is the scenario I described classed as deliberately causing it myself? Do I have to restart my Kaffarah because of the fast becoming invalide or is the fast still valid?

Fasting one day less due to going for umrah in Ramadhaan

Q: We went for umrah in Ramadhaan. We left a few days after Ramadhaan started.

South Africa fasted 30 days. Saudi also fasted 30 days. But they started Ramadhaan and finished one day earlier.

Because we were in Saudi for Eid, we only fasted 29 days in total actually.

So, do we need to keep qaza of one fast, because both countries had full 30 days but due to spending Eid in Saudi we only fasted 29?

Fasting qadha fasts in Shawwaal

Q: I missed two days of fasting in Ramadhaan due to menstruation and I have missed 15 days of fasting from the previous Ramadhaans. In order to obtain the reward of fasting six days in Shawwal, must I make up all 17 fasts first or only two?

In addition to this I forgot to keep the intention for some of the fasts of Ramadhaan, must I make an estimate and make up these fasts? If yes then should I do this also before fasting the six days of Shawwal?