Min nabo er hjælpsom og kommer bestemt, hvis jeg beder hende om hjælp med cyklen.

Because nabo is a common-gender noun in Danish, so it takes en words and the possessive form that goes with that pattern:

• en nabo = a neighbor
• min nabo = my neighbor

You would use mit with neuter nouns:

• et hus → mit hus

So this is about grammatical gender, not real-world gender.

No. Nabo can refer to a neighbor of any sex.

What tells you the neighbor is female here is hende later in the sentence:

• jeg beder hende = I ask her

So nabo is grammatically a common-gender noun, but that is separate from whether the person is male or female.

Because hjælpsom is a predicate adjective here: it comes after er and describes min nabo.

With a singular common-gender subject, the basic form is used:

• Min nabo er hjælpsom.

Compare:

• Et barn er hjælpsomt.
• Mine naboer er hjælpsomme.

So the form changes depending on what it describes.

Because Danish, like English, can leave out the repeated subject when the same subject belongs to both verbs.

Here, min nabo is the subject of both:

• er hjælpsom
• kommer bestemt

So the sentence means:

• My neighbor is helpful and definitely comes / will definitely come...

You could say og hun kommer bestemt, but it is less compact and not necessary here.

Here bestemt means something like definitely, certainly, or for sure.

It is functioning as an adverb, modifying kommer:

• kommer bestemt = definitely comes / will definitely come

Be careful: bestemt can also be an adjective in other contexts, but here it is not describing a noun. It is describing the action.

Because Danish often uses the present tense for future meaning when the context already makes the future clear.

In this sentence, the future idea comes from the condition:

• hvis jeg beder hende = if I ask her

So kommer naturally means will come here.

This is very common in Danish:

• Jeg ringer i morgen. = I’ll call tomorrow.
• Hun kommer senere. = She’ll come later.

Because hvis introduces a subordinate clause, and subordinate clauses normally keep the basic order:

• subject + verb
• jeg beder

So:

• hvis jeg beder hende ...

This is different from a main clause, where Danish often has verb-second word order.

For example, if you move the hvis-clause to the front, the main clause changes:

• Hvis jeg beder hende om hjælp med cyklen, kommer min nabo bestemt.

There, kommer comes before min nabo because the main clause is now after a fronted element.

Because the verb pattern is:

• at bede nogen om noget

This means to ask someone for something.

So:

• jeg beder hende om hjælp
• literally: I ask her for help

The parts are:

• hende = the person you ask
• om hjælp = the thing you ask for

This is a very useful pattern to remember:

• Jeg bad ham om råd. = I asked him for advice.
• Hun bad mig om penge. = She asked me for money.

Because hende is the object form of the pronoun, while hun is the subject form.

• Hun kommer. = She comes.
• Jeg beder hende om hjælp. = I ask her for help.

So after the verb beder, you need the object form hende.

Because om is part of the normal verb construction bede nogen om noget.

In Danish, you usually cannot leave it out here.

So:

• bede nogen om hjælp = ask someone for help

Not:

• bede nogen hjælp

This is one of those verb patterns that simply needs to be learned as a unit.

Because hjælp med noget means help with something.

So:

• hjælp med cyklen = help with the bike

The preposition med is the natural choice for practical help involving a thing or task.

Compare:

• hjælp med lektierne = help with the homework
• hjælp med bilen = help with the car

If you used om, it would sound more like help about a topic rather than help actually dealing with the bike.

Because Danish often uses the definite form when the thing is understood from the situation.

So med cyklen means something like:

• with the bike
• or in natural English, often just with my bike / the bike, depending on context

The speaker probably means a specific bike that both people can identify from the situation.

If you wanted to emphasize ownership, you could say:

• med min cykel = with my bike

But med cyklen sounds perfectly natural when the bike is already understood.

Not exactly a fixed expression, but it is a very natural combination.

It is simply:

• kommer = comes / will come
• bestemt = definitely / certainly

So together:

• kommer bestemt = definitely comes / will definitely come

You can use bestemt with other verbs too:

• Hun hjælper bestemt. = She definitely helps.
• Jeg gør det bestemt. = I’ll definitely do it.

So it is a flexible adverb, not a special one-off phrase.