Hello, two questions related to each other:
1) Whenever I want to update a task, first I enter its % complete. Then I update the current date of the project and then I go to Tools>Tracking>Update Project. For the tasks that are 0% its no problem and MS project pushes the start date to current date. But for the tasks I entered a % already, it splits the task which I don’t want. How can I prevent this separation, for tasks that are already started, when I update the project date?
2) Also, I want it to bring the black progress bar in the blue bar up to the current date automatically, when I am doing all these. How can I do that?
So far, since it is separating the tasks, I am first making actual and remaining duration as zero, then assign another actual and remaining duration, to make the bar continuous, but have to adjust actual duration manually in order to bring to the current data date. I want the actual duration (the black bar within the blue bar) to continue automatically from the start date up to current date.
And by the way there are no assigned resources to anything, so they are not affecting anything.

I'm guessing you are using the reschedule uncompleted tasks command to move remaining work forward to the status date? You can turn off the ability for Project to split tasks through Tools > Options, Schedule tab and deselect the option "split in progress tasks." However, that will leave remaining work in the past -- which sort of defeats the purpose of reschedule. Have you tried selecting 0 or 100% in the reschedule command?

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The black bar is percent complete -- if you are updating the percent complete the bar should be moving -- but you need to update the project. It will not assume because it is now Wednesday that you have progressed any. This is a manual update.