If a participant in a self-directed 401(k)/PSP decides to loan money from his or her plan account to a third party who is not a disqualified person or party-in-interest, is the loan subject to the "qualified loan" provisions, such as 5 year repayment and reasonable rate of interest?

Generally, no. But if the loan terms are unconventional (e.g. interest rate is below market rate) it raises the prospect that something else is going on. And the something else that is going on may be that the participant is getting some other impermissible direct or indirect, tangible or intangible benefit beyond the interest payments to the plan account. Or the participant might be getting a disguised distribution if the loan just happens to default and the plan has inadequate security or is otherwise unable to recover the money.