By default, HeaderContext FilterMenu is expanded down and its top edge is situated inside the HeaderItem. However, when the distance between the header item and the bottom of the current window is not enough for fitting the filter menu, it gets vertically relocated so that it stays inside the window.
If this is not the case and even if there is enough space below the header item, the filter still appears higher than expected, I would need to see more details on the current scenario in order to help you with troubleshooting. Please share the markup and code-behind of the aspx page containing the RadGrid so that we have a better overview and help.
Concerning the fact that the filter menu gets hidden by the RadMenu:
If the relocated filter menu collides with a RadMenu on the page, the RadMenu overlaps the filter menu due to its lower z-index.
To overcome that and keep the filter menu over the RadMenu, you check out the Controlling Absolute Positioning with z-index article, where you will find the initial z-index of different Telerik Controls and a few samples with overlapping controls. You can also check out the approach from Override the built in rules | RadHeaderContextMenu.
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