Ιs θα γράφω in the future tense? Is this θα it is formed with some sort of undeclined particle?
Yes, futute tense. There are 2 future tenses in Greek, Continuous ( Συνεχής): θα γράφω, θα γράφεις, θα γράφει, θα γράφουμε, θα γράφετε, θα γράφουν and Simple (Στιγμιαίος): θα γράψω, θα γράψεις, θα γράψει, θα γραψουμε, θα γραψετε, θα γράψουν.
This ψ comes from the theme γραφ+ suffix -σω=γράψω.
Why is "i will write if i want to" incorrect. It is the same sentence, same meaning even same words, just in a different order.
The word order you suggest is valid but there is no reason to change it from the original since identical word order in this case is correct in both languages. Such word order changes in the answers trick Duolingo into believing you do not know what you are translating. ;)
"I will write if I want" is correct current UK English - the "to" is implied. Too much literal translation does not help in learning any language. Could you modify the algorithms to be less literal and a bit more flexible?
Well, there are no algorithms that can be modified, when it comes to the actual grammar of the sentence. If a translation is grammatically correct and it matches the context of the main sentence, it's likely that it will be added.