Well, in fanfiction, anything can happen. It depends on the plot and the creativity of the writer. Maybe Shield stumbles upon some information about the Winchesters. But since fanfiction is not bound by the rules of the official shows, it could be a wild and unexpected scenario. For example, it could be through some supernatural event or a secret organization's files that Shield gets wind of the Winchesters.
Sure does. The Shield Hero slowly gains respect over time as he faces various challenges and proves his worth. His character development leads to others recognizing and respecting him.
One possible reason could be a conflict in ideologies. Spider Man might believe in a more individualistic approach to justice, while Shield's methods could seem too bureaucratic or controlling to him.
In the comics, Captain America's shield was created by a special alloy and given to him by the government as a symbol of his status and to aid in his fight against evil.
His relationship with Black Widow could also be affected. Black Widow has a long history with Shield. Spider Man might view her with distrust, which could lead to some interesting and conflict - filled interactions in the fanfiction. He may not be as willing to team up with her as he would be in the normal Marvel universe.
One idea could be that a character is on the bridge and is ordered to get off because there's a bomb planted there by Ultron. As they start the Shield run, they face various obstacles like collapsing structures. Another idea is that the 'get off the bridge' is part of a trap set by a rogue Shield agent. During the run, the main character has to figure out who to trust among the Shield agents.