What should I do if someone whose clothes are ritually impure sits next to me, whether that impurity transfers to me or not? And does a buckle or anything pure become ritually pure simply by being washed with water while wet, or must it be wiped with a tissue?

Impurity does not transfer between two dry bodies. However, if one of them is wet, there is a difference of opinion among scholars regarding its transfer. One must be cautious of obsessive doubt (waswasah), and impurity should not be judged as having transferred merely based on suspicion. So, if you sit next to a person whose clothes are impure, the impurity does not transfer unless there is certain contact between a wet impure spot and your garment, or your wet garment contacts an impure spot. To purify an impure object, water should be poured over it until it covers the impure area, and it is permissible to use it after washing and before drying.