You had the other launcher set as default. When you uninstalled it, it lost that default so it makes sense that you had to select the default home launcher after you uninstalled it.
As for the icons, a launcher does a lot of things and the app drawer, home screens, widgets and icons are all tied to that launcher. Uninstalling it means you need to set things up again for the default launcher.
Are the blank icons in your app drawer or on a home screen? If they are on the home screen, delete them and re-add them. If you had widgets, its very common for those to end up as blank icons after deleting a launcher. The big icons aren't something I have seen, but if they were on a home screen, changing the launcher could mess them up. Try deleting and re-adding them to the home screen and see if that fixes it.
If these problems are in your app drawer, go to:
Settings > applications > application manager > more > show system apps > touchwiz home > force stop > storage > clear data
Hit the home button. It will probably have you set Touchwiz Home as default again. That should fix any weird icons.