Household bleach works in a pinch, but don't make it a habit.
Yes, if it’s plain, unscented, no thickeners or splash-less additives. Check the label: sodium hypochlorite only, ideally 6% or higher concentration.
Pool shock is basically the same chemical but stronger and stabilized. Household bleach is weaker and degrades faster in sunlight. You’ll need to use more and it won’t last as long. There’s also a risk of introducing extra chloramines or other impurities if you grab the wrong bottle.
For one emergency shock while the pool store is closed? Fine. For regular maintenance? Just buy real pool shock. It’s cheaper per ounce of chlorine and way less guesswork.
If you do use bleach, add it at night and run the pump. Test your water the next morning.
Don’t reach for the Clorox with “splash-less” or “scented” on the bottle. That stuff has additives you don’t want in your pool.