Are Apple chargers replaced for free?

It depends. The chargers are covered under the same 1 year hardware warranty as the iPhone/iPad. If it is deemed a manufacturing defect, it could be replaced at no cost. Otherwise, if you had elected to purchase an AppleCare+ plan, it may be possible to get a replacement at a reduced cost.

I had my iPhone for less than 6 months, and Apple sent me a cable that is much shorter than the original one, and I had to pay about $20 for it.

I had owned electronics all my life, and I only have had problems with Apple cables. It's a pity because Apple products overall are built pretty strong.