Ik moet mijn tas nog inpakken voor de reis.

Because moeten is the infinitive, meaning to have to / must. After ik, you need the conjugated form:

• ik moet = I must / I have to
• jij moet
• hij/zij moet
• wij moeten

So in this sentence, moet is the correct present-tense form for ik.

In this sentence, nog means still or yet.

So Ik moet mijn tas nog inpakken means:

• I still have to pack my bag
• or I have yet to pack my bag

It shows that the action has not happened yet, but is still pending.

Because inpakken is the infinitive that goes with the conjugated modal verb moet.

In Dutch, with modal verbs like moeten, kunnen, willen, mogen, the main verb usually goes to the end in the infinitive:

• Ik moet werken.
• Zij wil komen.
• Wij kunnen zwemmen.

So:

• Ik moet = I have to
• mijn tas nog inpakken = pack my bag still / still pack my bag

That is normal Dutch word order.

Yes, inpakken is a separable verb:

• inpakken = to pack

In some sentences, separable verbs split:

• Ik pak mijn tas in. = I pack my bag.

But when the verb is used in the infinitive, as here after moet, it stays together:

• Ik moet mijn tas inpakken.

So:

• finite verb: often split → pak ... in
• infinitive: stays together → inpakken

Because mijn is the possessive adjective meaning my.

• mijn tas = my bag

mij means me, not my:

• Zie je mij? = Do you see me?

So:

• mijn = my
• mij = me

Voor de reis means for the trip or for the journey.

It tells you what the packing is related to. In other words, the bag is being packed for the trip.

• voor = for / before, depending on context
• de reis = the trip

Here it clearly means for the trip, not before the trip, although English may sometimes understand both ideas from context.

Because reis is a de-word in Dutch:

• de reis = the trip

Unfortunately, whether a noun takes de or het often has to be learned with the noun itself.

A useful habit is to learn nouns together with their article:

• de tas
• de reis
• het huis

Tas usually means bag. Depending on context, it can be a handbag, school bag, shopping bag, or travel bag.

If you specifically mean suitcase, Dutch more often uses:

• de koffer = the suitcase

So mijn tas inpakken voor de reis is understandable, but if you mean a proper suitcase, mijn koffer inpakken may be more precise.

Yes, that is also natural.

Both are possible:

• Ik moet mijn tas nog inpakken voor de reis.
• Ik moet nog mijn tas inpakken voor de reis.

The difference is subtle and mostly about emphasis.

• mijn tas nog inpakken puts nog close to the action of packing the bag
• nog mijn tas inpakken can sound like I still need to pack my bag with nog affecting the whole phrase a bit more broadly

In everyday Dutch, both are fine.

Yes. Dutch moeten can correspond to both must and have to in English.

• Ik moet gaan. = I must go. / I have to go.
• Ik moet mijn tas inpakken. = I must pack my bag. / I have to pack my bag.

In actual usage, English often prefers have to, while Dutch simply uses moeten.

Because after a modal verb like moeten, Dutch uses the bare infinitive, just like English after must.

Compare:

• Ik moet gaan. = I must go.
• not: Ik moet te gaan

So in your sentence:

• Ik moet mijn tas inpakken
• literally: I must my bag pack

No extra to is needed.

A simple breakdown is:

• Ik = subject
• moet = conjugated verb
• mijn tas = object
• nog = adverb
• inpakken = infinitive
• voor de reis = prepositional phrase

So the pattern is roughly:

subject + finite verb + object + adverb + infinitive + extra information

This is very common in Dutch sentences with a modal verb.

Yes. A few natural alternatives are:

• Ik moet mijn tas nog pakken voor de reis.
• Ik moet nog mijn tas pakken voor de reis.
• Ik moet mijn koffer nog inpakken voor de reis. (if you mean suitcase)

Here, pakken can sometimes be used more loosely in everyday speech, but inpakken is especially clear for packing.

So the original sentence is perfectly good and natural.