how close to a stop sign, or an intersection can I park
You want the back axles if trailer as close as you can to curb
Within 20 feet
The car did not park on the curb
you may not park next to a curb that is painted red.
From the Calfornia DMV web page on parking: When you park alongside a curb on a level street, the front and back wheels must be parallel and within 18 inches of the curb. Park parallel to the street if there is no curb.
There does not seem to be a fee for parking too close to the curb.
A driver must not stop in an intersection or on a road within 20 m of the nearest point of an intersecting road at an intersection with traffic lights. A driver must not stop in an intersection or on a road within 10 m from the nearest point of an intersecting road at an intersection without traffic lights.
You should park your car less than six inches away from the curb.
No you can not
Towards the curb.
yes. however make sure to check your state's specific definition of intersection. For example in Arizona the intersection is an extension of the curb lines. This is a much smaller area then in California where an intersection is defined by the crosswalk lines.