From the pictures, the case is fairly thick plywood, connected with dado joints. The drawers are likely the same material, and appear to be finger-jointed at the corners. This is good solid construction, and the woodburning pen won't produce anything more toxic than woodsmoke (which admittedly isn't entirely benign).
Yes. We have IKEA dressers in the bedroom similar to this, but made of solid pine. I had to reinforce the drawer corners when their patent fasteners started to loosen, but otherwise they are holding up fine after 25 years or more.
Even their particle board Billy bookshelves have lasted for decades (and counting) with a full load of books. I get the impression that most IKEA stuff is thrown out when it is overstrained or the corners get chipped during a move,