Do both grids have the exactly same cell size? If yes did you try to crop both grids with your polygon?
Do you need to somehow work with the datasets or just display them in one map? As I know SAGA does not have the on-the-fly reprojection so you cannot display data with different coordinate systems in one map. QGIS can do this (and also has much better tools for creating map prints while SAGA is much better for both raster and vector data processing) and you can also use SAGA tools from QGIS but if you need to for example extract DTM values to points then you will need to reproject the shapefiles...
True, QGIS says that the image has following extent: Layer Extent (layer original source projection) 82.7604403252879450,-5.4469216342855411 : 106.2371643982362315,15.1626329932361728 and puts the image somewhere near India.
Do you mean shapefile files generated by Geofabrik? Does the readme file of the DTM contain any information about coordinate system?
I was curious why the screenshots provided by Dan show the HDF loaded as a single file while I get a dialog which layers to load. The reason is that my Saga from Artful repo is 2.3.1. Will have to add johanvdw/saga-gis PPA again and check what is new there.
for the 3D view you can use this tutorial: https://sagatutorials.wordpress.com/3d-visualisation/
What sort of data is that? Did you just use drag and drop the file to SAGA window or did you use some import module? For example - Sentinel 2 images are already in UTM/WGS84 projection so you do not see values like 14.47785268449, 50.089622769829 but rather 462648.930402, 5548725.998117 example for Prague, Czech Republic and EPSG:32633 aka WGS84 UTM Zone 33N http://spatialreference.org/ref/epsg/32633/
At least you should be able to use buffer feature to create "flood zones" along the rivers and then easily select all polygons intersecting these zones. I am using this feature in QGIS, but I am almost sure that also SAGA has a module for this.