Will this watch fit a small wrist (5 3/4"-6")?

The interior dimension of this watch and band is about 6.5 in. My wrist is about your size and I wear it 2.5 to 3 in. higher up on the arm. Unless you want to wear it higher or remove links, it will be too big.

can the battery help restore a fading indiglo light

Yes a new battery can restore a fading indiglo light! I've worn this watch for over 30 years and when the light starts to fade I just get a new battery. Bingo- wach is back to new!

The water resistance information confuses me. How can it be water resistant to 30 m, but "not withstand showering or submersion?" Thanks.

It does not withstand a shower, wore mine once in the shower band fell apart and does not work anymore Amazon only has a 30 day return policy so they tell you to go thru Timex and they give you a run around. Bought it in August it’s January and no one can do anything won’t buy another watch thru Amazon!!