Irrevocable Trust and HELOC loan

If an Irrevocable Trust owns the real estate, I know the Trust signs the Mortgage, but does the Trust also sign the Note or do I also have the Note signed individually by the borrower whose income was used to qualify for the loan?

You can have different people or entities on the note. If you are relying on the individual's income to qualify for the loan, then sure. IMHO, the trust should also sign the note.