Learn Hardcore Russian: Эта рецензия написана так ясно, что её приятно читать даже на рассвете. - This review is written so clearly that it is pleasant to read even at dawn.

Написана is the short passive participle of написать. In this kind of sentence, Russian uses it the way English uses is written or has been written:

Эта рецензия написана = This review is written / has been written

Russian normally leaves out the present-tense is, so there is no separate word for it. Because написать is perfective, написана suggests a completed action with a present result: the review now exists in a clearly written form.

Why is it ясно and not ясная?

Because ясно here means clearly, not clear.

ясная would be an adjective agreeing with рецензия
ясно works adverbially and describes how the review is written

So:

рецензия ясная = the review is clear
рецензия написана ясно = the review is written clearly

In this sentence, the second idea is what Russian wants.

How does так ..., что ... work?

This is a very common Russian pattern meaning so ... that ....

так ясно = so clearly
что её приятно читать = that it is pleasant to read it

So the structure is:

так + adverb/adjective ..., что + result

It introduces a result or consequence.