A reputable company should be glad to visit and inspect the apparent damage without charge. Be prepared to allow a more extensive inspection in areas where damage may be less apparent.
There are steps you can take to help prevent damage, though there is no surefire way to prevent all damage from occuring. Please see the preventative maintenance section.
This is a fairly complex question and there are several things to look for including:
The repair process can take as few as 2-3 days, but be ready for longer durations if damage is extensive.
There is no way to tell until the damage has been inspected in person. The costs vary depending on the location and extent of damage, and type of home.
Unusual geological, weather, or man-made forces can always negatively impact your foundation, however if you have a lifetime warranty on the job from a reliable contractor, your worries are minimal.