True spiders need some time to harden up just like most Arthropods. I usually wait 7 days to offer them food after a molt.
By american house spider do you mean Parasteatoda tepidariorum? If so, they are egg laying machines. I wouldn't worry to much about one egg sac, many more are coming I'm sure. I found one last summer with thirteen egg sacs in her web. I had to take pictures to get anyone to believe me lol.
This spiders web is actually not designed to ensnare prey falling into it, or flying into it nearly as much as it is designed to alert the spider of prey trying to navigate the portion of the web anchored to the ground, or below. From my experience prey very rarely actually get stuck to the cobweb, but instead bump against the silk strands, alerting the spider of their location. If you watch the spider capture prey, you will see it moves down a few strands, and waits for another signal, till it pin points where the prey is, then she will flip around backwards and start feeding sticky silk at the prey. This is one of my favorite spiders to watch, as they truely have some cool capturing skills, I think more advanced then Widows and false widows.
You can see 10 of the egg sacs in this image, one is freshly hatched with a swarm of slings around it. 3 are not in this image.
They can eat prey much larger then themselves. This gal below protected a crack at the bottom of my garage door. She caught this crane fly and dragged it up into her web. When she passed away, I counted 4 mature male giant house spiders, 3 male hobos, 2 unknown agelenids, and countless other bugs along with this crane fly. She was truly a beast of a predator.
They are fearless and bold in the face of danger. This E. ovata invaded the much smaller house spiders web, and tried to steal the meal. The house spider stood her ground and eventually chased the much larger E. ovata away with relentless attacks.