HI !
As you say "build" I assume you have compiled Cqrog from source.
After compile with lazarus-ide, or with command "make" in cqrlog directory (the source root) did you run "sudo make install" ?

"make install" copies all additional files (inc. help,images, etc) to /usr/share/cqrlog

1)
If you did compile cqrlog and then tried to start it from src/cqrlog either friom command line or from lazarus-ide/run command
It will complain about image.
It needs symlink "share" to be created to cqrlog directory (source root) for this kind of testing.
While being in source root directory (cqrlog) issue command
ln -s /usr/share share
After that you are able to start compiled Cqrlog with command
src/cqrlog
Or from Lazarus-ide/run

2)
May be caused by reason 1). Sometimes happen also when run inside of Lazarud-ide/debug but restarting usually works.

3)
"gear icon" means startup menu icon , I assume. I do not know what desktop you use (Linux has so many) but you should be able to right click start menu icon of Cqrlog and select from opening menu "send to desktop".