Thanks for your questions! We are very glad that you are using this forum get answers.
1. A security belt is not a “must-have” however it is highly recommended. We will be traveling in some busy cities, and the benefit to a security belt is that it is to keep in a secure place while in crowds. Wallets of any type (not familiar with a “secure wallet”) tend to be easier for pickpockets to get their hands on.
2. While we hoped to get some good hiking in, the planned schedule does not ultimately include much hiking. There will be much traveling and walking, sometimes with all our bags, and that might include some sweating. But generally, you do not need to plan for high levels of perspiration any days. Your host families could choose to bring you on a half day hike, however that is unlikely, given that the weather will feel very very cold to them.
Hope this is helpful! Feel free to add any follow up questions.
Cara and Shino