Indonesian verbs never change. Not for person, not for number, not for tense. Makan is eat, ate, eats, eaten, will eat and have eaten.
You are done with conjugation forever. What replaces it is a handful of words placed before the verb.
The three basics
Saya sudah makan. ‘I have eaten.’
Saya sedang makan. ‘I am eating.’
Saya akan makan. ‘I will eat.’
Same verb, three times, untouched.
Sudah is bigger than “already”
Sudah is the most used of the three, and it covers the whole English perfect. It is also a question on its own.
Sudah makan? ‘Have you eaten?’
You will be asked this several times a day. It is a greeting as much as a question, closer to “how’s it going” than to a genuine enquiry about your lunch.
Belum is the answer, not tidak
The opposite of sudah is belum ‘not yet’, and this is where English speakers go wrong.
Sudah makan? → Belum.
‘Have you eaten?’ → ‘Not yet.’
Answering tidak means ‘I do not eat’, full stop. It sounds like a statement of principle. Belum leaves the door open, which is what the situation almost always calls for.
Masih
Masih is ‘still’, and it pairs naturally with the others.
Dia masih tidur. ‘He’s still asleep.’
Masih jauh? ‘Is it still far?’
Dropping akan
If a time word already makes the future obvious, akan is usually left out.
Saya pergi besok. ‘I’m going tomorrow.’
Adding akan is not wrong, just unnecessary. Indonesian omits whatever the situation already supplies, and you will see this pattern everywhere once you notice it.
What you’ll actually hear
What the book says: Saya sedang makan. What you’ll hear: Aku lagi makan.
Lagi has almost completely replaced sedang in speech. Sudah shortens to udah, and often to a bare dah. Learn the written forms, expect the spoken ones.