De ochtend is het eerste dagdeel van de opvangdag.

Because Dutch nouns belong to two article groups:

• de-words: take de
• het-words: take het

In this sentence:

• ochtend is a de-word → de ochtend
• dagdeel is a het-word → het dagdeel

This is something you usually have to learn noun by noun. There is some patterning, but in practice learners often memorize the article together with the noun.

Eerste is the form used before a noun, where it means first as an ordinal adjective:

• het eerste dagdeel = the first part of the day

Eerst is usually an adverb, not a noun modifier:

• Eerst eten, dan werken. = First eat, then work.

So before dagdeel, you need eerste.

Dagdeel is a compound noun:

• dag = day
• deel = part

So dagdeel literally means part of the day.

It is commonly used for sections such as:

• de ochtend = morning
• de middag = afternoon
• de avond = evening

It sounds a bit more structured or administrative than just deel van de dag.

Dutch very often combines nouns into one compound word.

So:

• opvang = care, childcare, reception, shelter, depending on context
• dag = day

Together, opvangdag means something like the childcare day or the day at daycare/care in this context.

It is written as one word because Dutch compounds are normally written together. English often uses separate words where Dutch prefers one long compound.

Van de opvangdag is a prepositional phrase that tells you what the dagdeel belongs to.

So the structure is:

• het eerste dagdeel
• van de opvangdag

Together: the first part of the opvangdag

Here, van works like English of.

Dutch often uses the definite article when talking about a named part of the day as a category or time block:

• de ochtend
• de middag
• de avond

So De ochtend is ... sounds natural as a statement defining what the morning is within a schedule.

Without the article, ochtend would not sound right in this sentence.

The sentence has a very straightforward structure:

• De ochtend = subject
• is = verb
• het eerste dagdeel van de opvangdag = predicate/complement

So it works like:

• X is Y

This is very similar to English:

• The morning is the first part of the childcare day.

No. Opvang has a broader meaning than just daycare.

Depending on context, it can refer to:

• childcare
• after-school care
• shelter
• reception/accommodation

For example:

• kinderopvang = childcare
• vluchtelingenopvang = refugee reception/shelter

In your sentence, the context strongly suggests childcare/daycare.

Yes, that would be grammatical.

The difference is mainly nuance:

• deel = part, a general word
• dagdeel = a part of the day, a more specific fixed term

So dagdeel sounds a bit more natural if you are dividing a day into scheduled sections.

A rough English-friendly guide:

• ochtend → OCH-tuhnt
• eerste → AIR-stuh
• dagdeel → DAKH-dayl
• opvangdag → OP-fang-dakh

A few notes:

• The Dutch g/ch sound is the throaty sound in ochtend and dag
• Final d is often pronounced more like t
• In compounds, Dutch often gives strong stress early in the word

These are only rough guides, but they can help you get started.