(1) After creating the tasks list, to record the progress, I am filling the timesheet. Is it the correct way of recording progress of work?

Yes, absolutely

(2) In the above method, actually I am recording the % of planned days utilized and on the Gantt Chart % progress comes accordingly. Is there a way to actually record progress of actual work? Example : If I have already worked for 50% of days, but actually work has progressed for 30% only, can I show on Gantt Chart progress as 30% thus reflecting true progress?

Yes, you have to update left work (can be done on Timesheet or on Activity)
For instance, you are assigned 5 days to an activity.
You did 2.5 days (50% of assigned).
But 2.5 is not enough to finish.
So you change left work from 2.5 to (for instance to 6) so that you did 2.5 upon total of 8.5 (progress is about 30%)

NB : in most cases, entering left work is more accurate than trying to estimate current progress.