Query params can be passed by adding the query params object to NavigateTo action. To do this click on the JS mode for Action and update it as follows.
{{navigateTo("PageName", {"param": "value"})}}
These can be consumed on the destination page with appsmith.URL.queryParams.param
.
Key-value pairs can be stored within the local storage with the help of the StoreValue action. To do so pick the StoreValue action and provide the desired key and values. These can be consumed on the destination page with appsmith.store.key