As from your glasses prescription power you are having myopic astigmatism
in both eyes, with power in right eye more than the left eye. Myopia
is also called as short sightedness.
For your first question, whether you need to wear glasses continuously, Yes you need to wear glasses continuously.
For your second question, regarding difference in the clarity of vision in both eyes. This is because your corrected vision in right eye is 6/6 and in left eye is 6/6p. This is because of a condition called as ambylopia. The treatment of this condition depends on age of the person. If this is noticed early before 6-10 years it can be treated by occluding the normal eye and using the abnormal eye. You need to get examined by ophthalmologist to know whether it is ambylopia or not and treatment.