11 My shod horse has always been sensitive to stones. If I take his shoes off and find a trimmer or farrier to trim him how long will it be before he will be able to be ridden on gravel roads?

Your horse could be ridden immediately on stones if you buy hoof boots for him. How long would it be before he could be comfortably ridden without boots or shoes on gravel roads? Depends on the individual horse. Some handle any surface without any problems straight away, others will take anywhere from 1 - 2 years before their feet harden up. Some will only be able to handle all terrain types at certain times of the year-they could be sensitive to spring grass and have a minor laminitic episode and go through a phase of sensitivity to stones till the grasses dry out in the summer.
A small percentage of horses will always need to wear hoof boots for comfort on abrasive terrain because they have ongoing nutritional issues or long term internal damage to their feet.

12 I do a lot of competing and jumping on my shod horse. I use studs for grip in heavy going. Wouldn’t my horse slip too much if his feet were bare?

Much of the answer to this question can be found in answer to question 10. There are many horses now competing with bare feet in all disciplines including jumping and all of their riders say their horses have improved traction in heavy going when jumping compared to shod/studded horses. Have a look for the barefoot horses at the show and watch how they jump.