You will need to learn every word with its spelling. There are some rules but they are not enough to explain why words are spelled the way they are; spelling is historic. Something you will see for example in the next lessons is that active voice verbs in the first person always end in -ω, like κάνω-to do, θέλω-to want. No exceptions.
The accent shows which syllable is stressed in a word and is the first thing a Greek ear pays attention to. They simply do not understand if the stress is wrong. If you ask for a "táxi" the Greeks think that you want law and order because τάξη is order and taxi is ταξί
Αccent is used
with all words which have more than one syllable if they are written in lower-case letters
with one-syllable question words to distinguish them from pronouns or conjunctions: πού/where, που/ that, who
with words written in capital letters when the stress is on the first letter
It is a good idea to learn the stress, orthography and gender (if a noun) together with every new word
Hello. As a contributor, I would like to let you and all the other learners know that there is absolutely nothing wrong with looking at the hints. In fact, in many exercises, looking at the hints is the only way for a learner to be introduced to newly seen words. This is why the team is particularly careful and diligent with them, as we expect learners to look at them and learn from them. Besides, in many cases, looking at the hints can give you not only an idea of possible synonyms or constructions you may not have been aware of, but also warn you about what synonyms have been entered into the database so far, so that you avoid getting your answer marked wrong because of it.
Of course, trying to complete an exercise is a great way to test your memory, once you've gone through a lesson, if you wish, but in no means is looking at hints considered cheating on this platform.
This skill is intended to familiarize the learner with the Greek alphabet, there is no set/authoritative formula for the English equivalent letter.
Read the other comments on this page to get some idea of which letters we equate with the Greek. This, in particular, should help: https://forum.duolingo.com/comment/22040507