Hi Erik,
Query 1: "can I change the map projection"
Yes. We can change the map projection using the property called LayoutType. If the LayoutType is Tile then it will render the maps in Mercator projection and LayoutType is Default then it will render in Equirectangular projection. We suggest you to use below code to acheive your requirement.
<syncfusion:SfMap>
<syncfusion:SfMap.Layers>
<syncfusion:ShapeFileLayer LayoutType ="Tile" Uri="Namespace.world.shp"/>
</syncfusion:SfMap.Layers>
</syncfusion:SfMap>
Query 2 : "combine the ImageryLayer with the ShapeFileLayer"
We have created a separate incident for further follow up's about “Combine ImageryLayer with ShapeFileLayer” under your Direct-trac login account.
https://www.syncfusion.com/account/login?ReturnUrl=/support/directtrac/incidents
Regards,
Sri Gayathri.