ऑफिस से आने के बाद मैं आराम करती हूँ, और फिर खाना बनाती हूँ।

Because Hindi uses the pattern verb stem + ने/ना form in oblique + के बाद to mean after doing X.

So:

• आना = to come
• आने = the oblique form used before a postposition
• के बाद = after

Together, आने के बाद means after coming.

So ऑफिस से आने के बाद literally means after coming from the office.

Here से means from.

So:

• ऑफिस = office
• ऑफिस से = from the office

Hindi uses postpositions like से, में, को, पर, which come after the noun, unlike English prepositions, which come before.

So:

• ऑफिस से आने के बाद = after coming from the office

Because this is not a normal finite verb here. In आने के बाद, the word आने is part of a verbal phrase meaning after coming.

A useful pattern is:

• करने के बाद = after doing
• खाने के बाद = after eating
• आने के बाद = after coming

So आने is used because it is the form that fits before के बाद.

In Hindi, the subject is often understood from the main clause.

So in:

• ऑफिस से आने के बाद मैं आराम करती हूँ...

the person who comes from the office is understood to be the same मैं from the main clause.

This is very natural in Hindi. English often also does something similar:

• After coming home, I rest.

You do not repeat I inside after coming home, but it is still understood.

Yes, आराम is basically a noun meaning rest or comfort, but Hindi very often makes verbs by combining a noun with करना.

So:

• आराम करना = to rest
• literally, something like to do rest

This is extremely common in Hindi. Other examples:

• काम करना = to work
• सफ़र करना = to travel
• कोशिश करना = to try

So मैं आराम करती हूँ means I rest or I take rest.

Because the speaker is female.

In the present habitual, the verb agrees with the subject’s gender and number:

• मैं आराम करता हूँ = I rest. (male speaker)
• मैं आराम करती हूँ = I rest. (female speaker)

Likewise:

• मैं खाना बनाता हूँ = I cook. (male speaker)
• मैं खाना बनाती हूँ = I cook. (female speaker)

So the sentence is being said by a woman.

Usually no. This form is the habitual present, not the present continuous.

So:

• मैं आराम करती हूँ = I rest / I usually rest
• मैं खाना बनाती हूँ = I cook / I usually cook

This sentence sounds like a routine or usual sequence:

After coming from the office, I rest, and then I cook.

If you wanted I am resting right now, Hindi would normally use:

• मैं आराम कर रही हूँ

And for I am cooking:

• मैं खाना बना रही हूँ

Here खाना means food or meal.

That is because it is paired with बनाना:

• खाना बनाना = to cook food / to prepare a meal

Hindi has many words that can be both a noun and a verb form depending on context. Compare:

• मुझे खाना है। = I have to eat / I want to eat.
  Here खाना is verbal.
• खाना तैयार है। = The food is ready.
  Here खाना is a noun.
• मैं खाना बनाती हूँ। = I cook food.
  Here खाना is also a noun.

They do slightly different jobs:

• और = and
• फिर = then / after that

So:

• और फिर = and then

This is very natural because the sentence is showing a sequence of actions:

1. come from the office
2. rest
3. then cook

You could sometimes omit one of them, but और फिर sounds smooth and clear.

Yes, that is also correct.

Hindi word order is flexible enough that both of these are natural:

• ऑफिस से आने के बाद मैं आराम करती हूँ...
• मैं ऑफिस से आने के बाद आराम करती हूँ...

Putting ऑफिस से आने के बाद first emphasizes the time/background setting: after coming from the office...

Putting मैं earlier can feel a little more neutral or speaker-focused.

Both are fine.

हूँ is the present-tense form of होना for मैं.

In the habitual present, Hindi commonly uses:

• participle-like form + होना

So:

• करती हूँ
• बनाती हूँ

The हूँ helps complete the present-tense meaning.

Compare:

• मैं करती हूँ = I do / I usually do
• वह करती है = she does / she usually does
• हम करते हैं = we do / we usually do

So हूँ matches मैं.

Yes. A common Hindi word is दफ़्तर.

So you could also say:

• दफ़्तर से आने के बाद मैं आराम करती हूँ, और फिर खाना बनाती हूँ।

Both ऑफिस and दफ़्तर are common.
ऑफिस is very widely used in everyday speech, especially in urban Hindi.