Η τεκμηρίωση είναι σωστή, παρόλα αυτά η απόφαση δεν είναι έτοιμη.

Η is the feminine singular definite article, meaning the.

Both τεκμηρίωση and απόφαση are feminine singular nouns, so each one takes η:

• η τεκμηρίωση = the documentation
• η απόφαση = the decision

Greek uses articles very regularly, so if a noun is definite, you normally include the article.

Because they must agree with the nouns they describe.

Here:

• τεκμηρίωση is feminine singular, so the adjective is σωστή
• απόφαση is feminine singular, so the adjective is έτοιμη

This is adjective agreement in gender, number, and usually case.

Compare:

• masculine: σωστός, έτοιμος
• feminine: σωστή, έτοιμη
• neuter: σωστό, έτοιμο

Yes. In this sentence they are predicate adjectives, not attributive adjectives.

• η σωστή τεκμηρίωση = the correct documentation
  Here the adjective is directly attached to the noun.
• η τεκμηρίωση είναι σωστή = the documentation is correct
  Here the adjective comes after είναι and describes the subject through the verb to be.

Same idea with:

• η έτοιμη απόφαση = the ready/prepared decision (less natural in many contexts)
• η απόφαση είναι έτοιμη = the decision is ready

It means something like nevertheless, even so, all the same, or however.

It connects two ideas:

• the documentation is correct
• despite that, the decision is not ready

So it introduces contrast, but a slightly more concessive kind of contrast than simple but.

You may see both.

• παρόλα αυτά is very common in everyday writing
• παρ’ όλα αυτά is also very common, and many teachers and style guides prefer it

As a learner, it is good to recognize both as the same expression meaning nevertheless / despite all that.

Because δεν normally goes before the verb to make the clause negative.

So:

• είναι έτοιμη = is ready
• δεν είναι έτοιμη = is not ready

Greek negation usually works by negating the verb, not the adjective by itself.

In normal, clear Greek, you keep it:

• Η τεκμηρίωση είναι σωστή, παρόλα αυτά η απόφαση δεν είναι έτοιμη.

Each clause has its own verb:

1. η τεκμηρίωση είναι σωστή
2. η απόφαση δεν είναι έτοιμη

Leaving out the second είναι would sound incomplete here. Greek does omit things sometimes, but not in this sentence in standard usage.

Because this is a new clause with a new subject.

Greek does not skip the article just because a noun has already been mentioned elsewhere. The second clause needs its full subject:

• η απόφαση δεν είναι έτοιμη

So the structure is very natural:

• subject + verb + adjective,
• then connector,
• then new subject + verb + adjective.

Yes, Greek word order is fairly flexible, though not completely free.

The sentence you have is neutral and natural:

• Η τεκμηρίωση είναι σωστή, παρόλα αυτά η απόφαση δεν είναι έτοιμη.

Possible variations include:

• Η τεκμηρίωση είναι σωστή, όμως η απόφαση δεν είναι έτοιμη.
• Παρόλα αυτά, η απόφαση δεν είναι έτοιμη.
• Η απόφαση, παρόλα αυτά, δεν είναι έτοιμη.

The meaning stays similar, but the emphasis changes slightly.

Yes, often you can.

• παρόλα αυτά = nevertheless / even so
• όμως = but / however

So:

• Η τεκμηρίωση είναι σωστή, όμως η απόφαση δεν είναι έτοιμη.

This is very natural Greek.
The difference is that παρόλα αυτά emphasizes despite that fact, while όμως is a more general contrast word.

Because παρόλα αυτά is linking two clauses and works like a discourse connector such as however or nevertheless in English.

The comma helps separate:

• the first statement: Η τεκμηρίωση είναι σωστή
• the contrasting follow-up: παρόλα αυτά η απόφαση δεν είναι έτοιμη

In writing, this punctuation is normal and helpful.