A stitch in time saves nine.
Let's say you have a shirt and the stitching begins to come apart, under the arms. You ignore it and continue to wear the shirt because the ripped part is concealed under the arm and no one can see the tear.
But, after a few uses, the rip in the shirt would become bigger. You would now need to stitch the shirt because the ripped part would be visible to others. The tear would be bigger than it was when you first noticed it. You would now have to spend more effort correcting it. Had you fixed the tear when you first noticed it you would have needed just a couple of stitches, but now you need to use more stitches to fix the bigger tear.
What the proverb means is that things should be done at the appropriate time. Don't wait for them to become a bigger problem before you react. You'll end up putting in more effort.
A barking dog never bites -
Generally, dogs that bark, do not bite, dogs that bite bare their fangs, growl and show aggressive behaviour. Dogs bark to let you know that you are in their territory or to warn others of the threat that the dog sees.
This idiom means that people, who threaten you frequently, rarely act. They make just empty threats.
Underestimate me...that'll be fun!