So here're the results - the airplane is finished and ready-to-play-with. Which the baby boy is doing now. Or more likely going to do one day - right now it's more about playing with details, especially rubber and plastic caps/wheels, and turning, and rolling, and pulling.
That LEGO Duplo little man on next pics is here only to give you the idea of scale - it's not that big, as you see.
The assembling was very easy because of mortices I cut prior to put wings & Co. I put a bit of strong glue into each mortice, and inserted the wings and other outstanding elements, paying attention that it doesn't squeeze out too much. Let it dry. And I made sure to put some blocks under the wings so that the latter can be parallel as they should be. The mortice were slighly larger than my wood pieces (I only had a smallest chisel of 6 mm large, hence the chopped mortice was 6 mm large, but my wood pieces were about 4 mm thick), so I filled the gaps one more time with glue and let it dry another night. Then I put it upside down and glue the rubber supports with wheels.