Νιώθω καλά τώρα.

A good approximate pronunciation is:

• Νιώθω → NYO-tho
• καλά → ka-LA
• τώρα → TO-ra

A few useful notes:

• θ sounds like th in think, not like th in this
• The accent marks show where the stress goes:
  • Νιώθω → stress on the first syllable
  • καλά → stress on the last syllable
  • τώρα → stress on the first syllable
• In Modern Greek, ο and ω are pronounced the same

Because Greek often leaves out subject pronouns when they are already clear from the verb form.

Here, νιώθω already means I feel, so adding εγώ for I is usually unnecessary.

• Νιώθω καλά τώρα. = normal, natural
• Εγώ νιώθω καλά τώρα. = possible, but more emphatic, like I feel fine now

This is very common in Greek.

Νιώθω is:

• present tense
• first person singular
• from the verb νιώθω = to feel

So the ending -ω here tells you the subject is I.

This is one of the most basic present-tense verb endings in Greek.

Because καλά is being used as an adverb, not an adjective.

In this kind of expression, Greek uses καλά to mean something like well / fine after verbs such as:

• νιώθω = feel
• είμαι = be

So:

• Νιώθω καλά = I feel well / fine
• Είμαι καλά = I am well / fine

By contrast:

• καλός / καλή / καλό are adjective forms and describe a noun
  For example:
  • καλός άνθρωπος = a good man
  • καλή μέρα = a good day

So in this sentence, καλά is the correct form.

Τώρα is an adverb of time, meaning now.

Yes, it can move. Greek word order is fairly flexible, and moving τώρα changes emphasis more than basic meaning.

For example:

• Νιώθω καλά τώρα.
• Τώρα νιώθω καλά.
• Νιώθω τώρα καλά. (less common, but possible in the right context)

The most natural alternatives are usually the first two.
If τώρα comes first, it often gives a little more emphasis to now.

Both.

That is one reason νιώθω is such a useful verb. Depending on context, it can refer to:

• physical state
  
  • Νιώθω καλά. = I feel fine
• emotional state
  
  • Νιώθω χαρούμενος / χαρούμενη. = I feel happy
• general sensation or perception
  
  • Νιώθω κρύο. = I feel cold

So in this sentence, the exact nuance depends on context, but it works naturally for either physical or emotional well-being.

They are very close, and in many situations they can replace each other.

• Νιώθω καλά τώρα.
• Αισθάνομαι καλά τώρα.

Both are correct.

The main difference is tone:

• νιώθω is often a bit more everyday and conversational
• αισθάνομαι can sound a little more formal or more standard, though it is still very common

A learner will hear both a lot.

Yes, absolutely. Είμαι καλά τώρα is also very natural.

The difference is small, but this is a useful way to think about it:

• Νιώθω καλά τώρα focuses more on how I feel
• Είμαι καλά τώρα focuses more on my current condition/state

In everyday conversation, both can work in many of the same situations.

For example:

• after being sick, either one could sound natural
• after a difficult emotional moment, either one could also work

If you want to highlight the experience of feeling better, νιώθω καλά τώρα is especially natural.

It is neutral everyday Greek.

It is not slang, and it is not especially formal. You can use it in:

• normal conversation
• messages
• casual replies
• many everyday situations

So it is a very useful sentence pattern to learn.