My Delphi programs are showing as HEUR/AGEN virus

if Delphi on your pc is infected, then you might be producing that problem
might also be that's it been infected so long and the Avira has only just figured this out

i'd take a backup of the Delphi folder
and then run Avira on it to see

And as suggested report all finding to Avira.

Delphi is an excellent tool to write malicious software
Wouldn't be the first time .exes produced by Delphi are marked as virus

One (very) time ago, there was some infected Delphi components - and result of installation was - infected Delphi (files).
Then - each produced exe - contain virus too.
Try to install Delphi somewhere else, and try to rebuild your code.
Additionally, you can check recent modified files in Delphi installation folder, or reinstall complete Delphi once again.

if files in you're delphi installation bin folder are "touched" and their date was modified
then your delphi won't start anymore

delphi has a builtin check for last write dates in the bin folder to see if it's compromised
it's more of a license check actually