Hi Marco, Such a nice and brilliant idea. Its possible to implement and its viable one to reduce food waste redirecting to those people who need it. How to build trust: You can start by creating a free event and letting people contributing what they have. When they come to deliver or you collect from their points you can ask on ways to increase trust on allocation. Theoretically is letting contributor feel the decision of supplying and proud of where will it be consumed. Take photo events when you are feeding people and let stakeholder know.
Written contract: I think since its a volunteer its difficult and people are providing things which are over exceeding. In food its a difficult one as people will opt to store for future use. So volunteering and alerting those stakeholders on ways their contribution is used is better one.
Food storage: Since food rescue program aim at feeding people (and eating is a daily need), its better not to store but provide to all people on the same day. I believe people will provide food with mostly nearly expired date (though expiring date does not mean food in not good to be consumed within few days after expire e.g. bread, but rotten food is another thing which can't be consumed).
Create a collection point for people in need (e.g.street children and homeless people) and for those disabled one you can have a simple means deliver to their places every after very two/three days depending on capacity.