All of the described issues occur because the example is using server operations for paging and sorting, but not for grouping. When serverPaging has used the Grid will request the data only for the specific page, but as the grouping is made client side, it will be made only of the available items on the page, as it does not have all of the data available.
In this scenario I can suggest two approaches:
1) Enable serverGrouping as well. Please have in mind that this will require additional code on the server that will handle the request and return the grouped data in the expected format:
2) To remove the other server operations and have all of them on the server. The Grid will still be with a remote data, but the operations will be done on the client(the Grid will request all of the data at once):
Please have in mind that we recommend all operations to be done either on the client or on the server as mixing them can lead to the described issues and more.
I hope this will help to achieve the desired result.
Telerik by Progress