Schengen Visa Refusal from the Spanish Consulate

While you don't give us much to work with in the way of describing what you did provide, generally speaking, people who receive refusal number 2 didn't really understand what was being asked for.

They will come and post that they gave a bunch of information. Take a look at this question, for example. He gave what appears to be an over-abundance of information to the CBO and then wonders why on earth he was refused.

[EDIT] I would add, as a friend of mine who read this answer pointed out, "why should the applicant spell it out exactly like you suggest, after all, they are applying for a visa designed for short term tourism..." My answer is that the CBO might still question why the visit is needed. Is the applicant intending to come to look for work, to visit family, to relocate, or tourism? Without an explicit statement of the reason for the visit, the CBO then has to look at everything else with an eye to figuring out the 'real' reason. By stating tourism, the CBO can look at everything else with an eye of "does the rest of the application fit the specific intent" which is (potentially) easier to determine. And after all, we are seeing refusals.
[End of EDIT]

As I pointed out in my answer to that question, what he didn't give was the reason for the trip. By justification, what they mean is the reason for taking the trip (or as Gayot Fow says in his answer, the premise of the trip.

So, my best guess here as to why you were refused, assuming you were carefull and gave them everything else they've indicated you needed to provide, was that you forgot to explain the why. Be sure to include a short explanation describing why you want to make the trip in the first place.

This can be as simple as a short paragraph stating that "I plan to tour Barcelona and Madrid, perhaps see a flamenco show and try some Spanish food. This will be a much needed vacation from my work."

Then, when your paperwork is viewed by the Officer, when he asks himself "Why is this person wanting to come into Spain?", he has the answer.

I can't find any reference where they say an appeal HAS to be translated, but (as long as it is an accurate one) providing a translation shouldn't hurt.

When you see "Justification for the purpose and conditions of the intended stay was not provided" on a Schengen refusal, it usually means that the applicant failed to establish the premise of the visit.

"Premise" is best explained by looking at some of its constituent parts. This diagram can be helpful...

These are some of the things the decision-maker considers when evaluating an application. What they amalgamate to is a 'big-picture' question like "Why are you doing this?" and "Why are you doing this now?" Those questions need to be answered in a way that makes sense given everything else that is known or implicitly concluded about the applicant.

You did not provide all of the personal information and evidence that would be needed to retrace what the decision-maker was thinking (and we don't want to see that stuff anyway), but it is fairly certain that given your age, gender, apparent lifestyle, and all the rest that your visit did not seem consistent.

I do not have an exhibit for the second reason: "Information submitted regarding the justification for the purpose and condition of the intended stay was not reliable", but it means the quality of your evidence was below their standard. Perhaps your bank statements were not on the approved list of banks? Or there were strange transactions? Perhaps your sponsor's letter did not contain all the needed information? They do not go in to detail when they give this reason, it's down to you to upgrade your evidence.

Having said that, your question is whether or not to appeal the decision. If you have lots of evidence that helps establish your premise which you did not submit originally, then it is probably better to make a fresh application and spend some time addressing all the relevant points in the diagram above. On the other hand, if you think the decision-maker failed to consider evidence that you did provide, then appeal is a good option.

But if they think you are trying to convert the appeal into a second application... If you try to appeal with a strategy of introducing new evidence, you may lose and the result will be waste of time. Wasting time dilutes an important part of the premise "why at this particular time?" and if the appeal goes on for a long time you may have to think up something else to bolster your premise.

Also, since you got two hits, the risk assessment kicks in and portions of this answer become relevant. This will also play heavily in an appeal and they may decide to uphold their decision even if you are right. If you think this may happen, it's better to pause and make a fresh application that carefully belabours all of their concerns.

For your final question, you did not identify your native language or where the Spanish consulate is based, so that leaves translation up in the air. Generally, if you are preparing an appeal bundle, it should be rigorously translated if they require it or not. That's an opinion informed by best practices; it may or may not be a statutory requirement.