-Technically, you can not have gap.
2. 如果人在U.S.,是不是在兩公司的PAYROLL上的GAP不能超過10天?
-Same as question 1.
3. 如果人不在U.S.,是不是就不存在GAP的問題了?
-是不存在GAP的問題. Because you use new H-1 visa to come back, your H-1 status is a new one (not related to your previous status).