The convergence failures as well as the interruption do not necessarily have an influence on the result. Please check your courses. If there are jumps, you can not explain, they may be caused by convergence failures.
In your second case your calculation crashed because of some convergence problems. For further information see here:viewtopic.php?f=15&t=494viewtopic.php?f=15&t=789viewtopic.php?f=15&t=439viewtopic.php?f=15&t=768
To reduce the number of grid elements usually is no good way to get the calculation to run as the accuracy of the result will decrease in most cases.
Please also go to Computational Parameters -> Enhanced and see the table "solver settings". If not yet done, try to change the value URF - RH from 0.7 to 0.3. That handles the influence of the last result to the next step and often leads to a better convergence behavior.