Concerning your wheelbarrow: Do your self a big favor and forget the
concrete. Even if you could fill it evenly so it didn't go wop-wop-wop
when you pushed it, every time you hit a bump you wrists will take the
beating. I had a barrow with a metal wheel (some kind of antique I found)
that taught me a lesson.
If you have a flat in a new inner tube you probably pinched it during
installation. I've done this to bicycle tires many times. But I had your
problem with my wheel barrow and found there was a hawthorne thorn still
in the tire that punctured the new tube. Run your hand around the inside
of the tire to make sure you remove the original problem.