A quick glance at the specs looks like a decent steel frame done up with low grade components. Upgrading piece by piece will likely result in a decent bike - most of the issues you identify are fixable, and the rear brake may just need new pads and an adjustment - but this might not be your best value. New components cost more as parts than by buying a whole bike at once. And for a 43km/day routine, a lighter weight frame might be desirable.

$750-$1000 will certainly get you a very nice used bike if you can find something that'll work for you. Make sure you have a repair allowance left, though, since you'll probably find at least a few components on any used bike are ready for replacement.