Hi Sergey!
Regarding your first two questions on whether 1. you can get a payments list by ID/Timestamps and 2. getting a payments list from last year. We currently do not support these yet.
However, we will take this into account and will keep you up to date when we have made any changes to this.
A solution for getting 'only new payments' could be via pagination https://doc.bunq.com/api/1/page/pagination.
The future_url can be used to refresh and check for new items that did not exist when the listing was requested.
Let us know if this works for you😊✨