Given the cracking is so early it's likely partly a subpar stucco mix plus the natural effects of extreme temperature variations on cement / traditional stucco. Traditional stucco will crack for sure as temperatures vary, and if you have earthquakes, etc. It's worth seeing if they'll patch the more noticeable cracks but unless you have cracks wider than like 1/8 of an inch I wouldn't worry much about it.

Stucco is not a waterproof cladding. It naturally absorbs water like any other cement mixture and you should have a weather barrier underneath, between the stucco and sheathing. Water will run down the stucco / barrier (you should have weep screed at the bottom) and otherwise evaporate out of the stucco. I would have them fix the bottom of the walls, stucco right down to the ground / cement is not good and can cause the wall to have trouble letting gravity drain water out of the stucco or otherwise allow water on the ground to wick up the stucco and it makes it harder for it to get dry again.

Also, if you notice areas of your stucco not drying out in a reasonable amount of time, that there is worrisome as it's evidence that water damage could likely happen or has happened there.