Fate
Fun Street Avenue was the place to be on a summer afternoon. The street was named that because that was what it was. For five city blocks, shops and arcades lined both sides of the street.
Right now, the second sentence feels a bit redundant, because the third sentence explains the first (Why is it the place to be? Because there is roughly a quarter mile of arcades and shops!). Using more descriptive language to capture the character of the place and ground the reader might give these sentences a bit more interest (what should the reader see, smell, feel, taste?) and open the way to the rest of the narrative.
A Second Chance
The stench of rotting garbage made the area unbearable to breathe. For Justin, the smell didn't effect him as his sense of smell had been damaged. Dressed in ratty, dirty clothes, Justin rummaged through the garbage bins searching for anything that could be sold for money.
Yet again, I don't think the second sentence is really necessary. Instead, maybe try to ground the reader in the story. What time of day is it? Is he in a dump or on a garbage barge? How is Justin going to transport the items he finds? Does he have any protective gear on (like a bandana to filter the smell/taste of garbage or gloves?) Are two words necessary to describe his clothing? How does Justin perceive his clothing and how does it fit?
Until Death Do Us Apart
Beyond the wooden door, lived a creature so horrible, so foul, Jason feared nothing else. Every night he had to face that creature. Even his nightmares had nightmares about the creature.
You've established two characters here, Jason and the creature. I think that there's a lack of information for either one though. We know nothing about Jason, except that he's scared, and we know nothing about the creature, except that it's bad. Depending on the tone you're going for, you could jump into Jason's mind and have him confronting the monster (or running away) for a more
en media res approach or you could keep the omniscient storyteller feel by backtracking and explaining who Jason and the creature are in greater detail. Either way, the reader will want a little more to go off of
Overall, I think each of these openings have potential to be some pretty cool stories, but they need a little more development. An exercise I find really helpful is to grab an anthology in the genre I write in and look at the beginning sentences, then try to use some of the same techniques in my own writing. After practicing for a bit, you'll find your beginning sentences getting a lot tighter and more interesting
Good luck and welcome to the thread!