Greek is a "pro-drop" language, meaning the subject is not necessarily expressed overtly. This is because it can be easily inferred from the verb endings (e.g. -ω for active,-μαι for passive). English on the other hand is not a "pro-drop" language, so the subject must always be present.
For example, Spanish is pro-drop as well, but French is not.
I am reminded of the first ever sentence translated in modern times out of Ancient Hittite : "Now you have bread to eat and you have water to drink'. A nice parallel....
I'm sorry but I have to ask now: What's the difference between ι and η or between ο and ω?
They are pronounced the same but used to be pronounced differently many thousands of years ago -- that's why there are separate letters.
Nowadays, the spelling follows etymological/historical rules, so in many cases, you have to learn which letter to use.
It is very much like "ee/ea" in English -- "meet" and "meat" sound exactly the same for nearly all English speakers, though a few dialects still preserve a difference there. All others simply have to learn which word takes which spelling.
You're referring to the Greek, "πίνω" and "τρώω" both show they are "I" from the suffix "ω" on the verb. You could use εγώ= Ι, but it's really not needed and not often used. "Εγώ πίνω και εγώ τρώω..."
In the "body" of the word, you just have to learn the spelling.
It is like "ea" versus "ee" in English. Why do we write "leaf" but "beef", "seat" but "street", and so on when they sound identical?
There are historical reasons (the sounds used to be different), and this is true for Greek as well -- but in terms of the modern language, you just have to learn the spelling, because both Greek and English use a historical spelling.
In the endings, it's a bit easier, as grammar (not just history/etymology) can help you.
For example, a word ending in an /o/ sound will end in -ω if it's a verb but in -ο if it's a noun. (A bit simplified but mostly true.) Similarly, a noun eing in an /i/ sound will end in -η if it's feminine but in -ι if it's neuter. (Again, a bit simplified.)
The meaning is the same but the pronunciation is slightly different -- in a "type what you hear" exercise, you can't use that spelling if the voice says τρώω.
How can i know when to translate "πίνω νερό καί τρώω ψωμί" to "I'm drinking water and eating bread" rather than "I drink water and eat bread" ?
The last sentence was almost the same and translated to present participle form with the "ing" ending
Greek has only one present form and this sentence can be translated as either...
''I drink water and eat bread."
or "I am drinking water and eating bread." etc
Both forms are accepted for this sentence. If it was not accepted there might have been another problem since we can't see what you wrote you should send us a screenshot so we can understand what the problem was.