Problem #1 Dolphin doesn't find it's start-folder (solved)
Goto the dolphin-menu-bar choose "Adjustments" -> Start
lookup -> Start-Folder
What adress is inserted there?
pick "/home/USERNAME"¹ (without exclamation marks) or browse to it.
What was exactely right, was starting the program from commandline via Konsole. This gives hints. You can easily switch to reporting-language like this:
(this is valid for any program-then it returns the output in english and you don't need to translate it for publication). It's always prefered to have the output of the command in full.
(1) USERNAME must replaced with the real username -> Type in Terminal
whoami – to make sure it fits.
Problem #2 Dolphin can't be started from the menu
As you say, you can start Dolphin from Konsole - than the same error might appear in the .desktop file. This files resides in
/usr/share/applications/ . As normal user you can read it, but not change anything. This would need
kdesudo kate to edit & correct. I would recommend you to copy the current text-content & use paste.ubuntu.com to link this then to here.
This allows us to see if the contents are faulty. One of the rules of error-correction is doing a proper error-analysis (especially via distance).
A personal tip (that helped me lot): before you make any changes to the file, make a screencopy beforehand (KSnapshot). Such helps most times, if an error is worth qualifying for a bugreport or if you have to revert it to the previous state.