Either is correct. In Greek, the article is used much more than in English. In this case, it does sound better in English without the article because it is a general meaning. With "the" it would indicate a specific item.
I don't have Greek script yet, but why is the o sound in the first word skipped? Is it like a vowel blend in English where you just say the first one (like "boat") but here it's the second?
Are there any (simple) rules to how the various i sounds are written in Greek or is this all memorization?
There are no simple rules but there are some patterns, for example feminine nouns ending in an i sound are always written with η. You'll find these out as you progress.
A Dipthong: a combination of two vowels that make a unique sound. In Modern Greek the word Diphtong (δίφθογγος) refers to two vowels that make a sound like a simple vowel, and here are 8 of the sounds.
|Diphthong||. IPA .||How to say it|
|ει||[i]||key, bee, tree|
|οι||[i]||key, bee, tree|
|υι||[i]||key, bee, tree|
|αυ||[av], [af]||ranges from avenue, to afro, depending on letters before and after|
This is all the time I have at the moment. I will try to return to complete the table at another time.
Or perhaps someone else will come along and provide a better reference.
As you see in the IPA that sometimes they can make different sounds for the same characters being used.