What should I do to purify my clothes? Do I have to wash them seven times? And if, before the seventh wash, water touches a part of my body or garment, do I also have to wash it seven times, or is one time sufficient, given that pork and dog meat steam rose during lunch while I was sitting at the same table?

We can summarize the answer for you in the following points:

We advise you to disregard these whispers (waswas) and not to dwell on them. The steam rising from dishes containing pork or dog meat does not defile clothes or the body, even if you are certain it has touched them. There is no need to wash clothes or the body from this steam. Smoke and steam that have transformed from impurity are pure. The steam rising from bathrooms or foul gases emanating from impurities, if they cling to clothing, do not render it impure according to the sound opinion of the Hanafi school, and the other schools of thought do not differ on this matter.