No, if you're being compensated, that's pay. Otherwise it smacks of escorts' "You're paying me for time, anything that happens between two consenting adults ..." wink wink nudge nudge

"under the table" work doesn't mean you're not getting paid, it means your pay isn't reported to the relevant tax authorities. That doesn't make it less illegal.

Working for free is still working. It usually requires the right kind of visa and a work permit to remain legal. Do it on a tourist visa at your own risk.