Is there any way to generate custom errors/warnings in LaTeX?

For LaTeX, use the commands described in section 4.9 of clsguide.pdf:

• \PackageWarning and \PackageWarningNoLine if you are writing a package
• \ClassWarning and \ClassWarningNoLine if you are writing a class
• The internal generic version for warnigns is \GenericWarning

The expl3 bundle has another interface for warnings and similar messages, see Part XVII in source3.pdf.

Just use the built-in \errmessage for errors, e.g. \let\GenerateWarning=\errmessage.

The kind of warnings Latex generates are just messages; \let\GenerateWarning=\message will not interrupt the compile. Latex uses the commands \@latex@warning and \@latex@warning@no@lines to create these for its own warnings: you check the source you find in latex.ltx.

You can use \typeout{msg}. The command will print msg on the terminal and in the log file.