Articles and Superlatives – ‘It is Best’ vs ‘It is the Best’

Both of your examples

This is done easily.

This is done more easily than I thought.

are grammatically correct.

However, I would personally consider both sentences to be slightly awkward or incomplete, since you could express the same ideas using adjectives. If you had no more details to add, then more natural expressions might be

This is easy.

This task is easy.

This was easier than I thought.

This job was easier than I thought.

The original examples would also be fine if there were more details to complete the sentence, so that there is a reason to use the adverbial form rather than the simpler adjectives that I proposed above.

Calculating this antiderivative is easily done using integration by parts.

Calculating this antiderivative is more easily done using a trigonometric substitution.

Adding to @GoDucks' nice answer, when most means very, exceedingly or extremely as an intensifier, you should not use the definite article the. It could be a better explanation because there is a case where the is not used even though there is a noun after "most + adjective", i.e.:

This is most dangerous procedure.

The above sentence doesn't mean that the procedure is the most dangerous procedure of all the procedures. It just indicates a degree of danger that the procedure carries.

Therefore, whenever you see the word most without articles, you could try to replace it with the intensifiers I suggested above, i.e.:

Most (very, exceedingly, extremely) incredible is how many Islamic scholars have popped up over the past few years.

This is most (very, exceedingly, extremely) dangerous procedure.