When I've exported map images from QGIS I've always used the Print Composer (Project > New Print Layout..., or Project > Layouts > [your layout name] once you've created it). Once you've placed a map object in the composer, when you refresh it it will show the current map displayed in the editor filling the space you've defined on the canvas (which could be the entire canvas). You can select the coordinate system to export in by selecting the map object in the canvas and going to "Item Properties" on the right, which lets you pick the exported CRS (as well as the displayed map extents and a bunch of other settings). Finally, when you select "Export as Image" in the Print Composer's topbar after selecting the filetype and name to save you'll be able to enter the export resolution (at least for PNGs, which are all I've used it for).