I have calculated the uncertainty from repeated measurements. Is it possible to have an uncertainty value, which is lower than the accuracy (given in the specification) of the instrument?
The uncertainty of repeated measurement and calculation may be lower than the accuracy of the instrument, but the uncertainty of calculation should not be the whole of the measurement uncertainty.
The current preferred way to think about accuracy is a combination of type A and B components of Measurement Uncertainty.
This used to be referred to as bias (measurement error) or systematic measurement error if it remains constant, as well as precision (repeatability)
Thus, it is very likely that the one component of accuracy (repeatability) will be lower than the overall accuracy statement.
The caveat to this assumes we can trust the manufacturer's stated accuracy claims as some are very conservative and others, well, let us say, are not.
I highly recommend reading Introduction to Statistics in Metrology and the new Third Edition of the Metrology Handbook from ASQ for more information on this and other similar topics.
Yes IMO. as long as the test conditions/measurement procedures are not same compared to the manufacturers, The human error could not be neglected. another possibility is to confirm this uncertainty-accuracy variation is to conduct the same after calibrating the equipment.