The clock on the wall is two minutes faster. This one over here next to the fridge is accurate. この表現は自然ですか？

You would say 'fast' instead of 'faster', unless you swapped the sentence order like this:

"The clock next to the fridge is accurate. The one on the wall is two minutes faster."

You could use 'faster' in the above example because you're comparing the second clock's accuracy to the first's.