First of all, I would like to tell you that it is not possible to pursue degree course without qualifying +2 level of exam. So, if you want to pursue a degree course, you must complete your +2 level of studies.
As far as diploma course is concerned, yes, you can pursue it after qualifying 10th exam. The required percentage of marks depends upon the course, institutes/universities and various other factors. However, you must always try to do best and work hard to get a minimum of 60% marks for better future.