Der Fahrradständer hält das Fahrrad.

Because German nouns have grammatical gender, and the article has to match the noun.

• der Fahrradständer = the bike stand / bike rack
• das Fahrrad = the bicycle

There is no special reason in this sentence itself; these are simply the genders of those nouns, and you need to learn them with the noun.

A helpful tip:

• words ending in -er are often masculine, so der Ständer fits that pattern
• das Fahrrad is a neuter noun, so it takes das

German very often combines nouns into compound nouns.

Here:

• das Fahrrad = bicycle
• der Ständer = stand

Together:

• der Fahrradständer = bicycle stand / bike rack

In German, these are usually written as one word, not as separate words like in English.

Also, the last part of the compound usually decides:

• the gender: der Fahrradständer
• the plural pattern

So even though Fahrrad is das, the full compound is der because the final part is Ständer.

Because das Fahrrad is the direct object of the verb hält.

In this sentence:

• Der Fahrradständer = the subject, the thing doing the action
• hält = holds
• das Fahrrad = the direct object, the thing being held

That means das Fahrrad is in the accusative case.

For das, nominative and accusative look the same:

• nominative: das Fahrrad
• accusative: das Fahrrad

So the form does not change here, even though the case does.

Also:

• dem Fahrrad would be dative
• den Fahrrad is not correct, because Fahrrad is neuter, not masculine

Because the subject is der Fahrradständer, which is third person singular: it.

The infinitive is halten = to hold

Its present-tense forms are:

• ich halte
• du hältst
• er/sie/es hält
• wir halten
• ihr haltet
• sie/Sie halten

So with der Fahrradständer (= he/it grammatically), you need:

• Der Fahrradständer hält das Fahrrad.

Because halten is a strong verb that changes its stem vowel in some present-tense forms.

Specifically:

• a changes to ä in the du and er/sie/es forms

So:

• ich halte
• du hältst
• er/sie/es hält

This is something you just have to learn with certain verbs. Other common verbs do similar things, for example:

• fahren → du fährst, er fährt
• laufen → du läufst, er läuft

Not usually.

A Fahrradständer normally means:

• a bike rack
• a bicycle stand
• something that holds a bicycle upright

A kickstand on the bicycle itself is more commonly:

• der Fahrradständer in some contexts, but this can be ambiguous
• often more specifically der Seitenständer = side stand

So Fahrradständer can sometimes be understood as a stand attached to the bike, but very often learners will hear it used for an external stand or rack.

Because German main clauses usually follow the verb-second rule.

In a normal statement:

1. first element
2. conjugated verb
3. the rest

Here:

1. Der Fahrradständer
2. hält
3. das Fahrrad

So the structure is completely normal German word order.

You could also move another element to the front, but then the verb still stays second, for example:

• Das Fahrrad hält der Fahrradständer.

That sentence is grammatical, but it sounds marked or unusual in normal conversation because it emphasizes das Fahrrad.

A rough English-friendly guide:

• Der ≈ dare (but shorter, with a German r)
• Fahrradständer ≈ FAHR-raht-shten-der
• hält ≈ helt with a more open vowel, something like hehlt
• das Fahrrad ≈ dahs FAHR-raht

A few details:

• ä in hält and Ständer is somewhat like the e in bed, though exact pronunciation depends on accent
• st at the beginning of a syllable is often pronounced sht, so Ständer sounds like SHTEN-der
• the d at the end of Fahrrad sounds closer to t in actual pronunciation

Yes. Halten is a very common German verb with several meanings depending on context.

Some common ones are:

• to hold / support
  
  • Der Fahrradständer hält das Fahrrad.
• to stop
  
  • Der Bus hält. = The bus stops.
• to keep
  
  • Bitte halten Sie Abstand. = Please keep your distance.
• to consider / think in some expressions
  
  • Ich halte das für richtig. = I consider that correct.

So in this sentence, hält means something like holds, supports, or keeps upright.

The plurals are:

• der Fahrradständer → die Fahrradständer
• das Fahrrad → die Fahrräder

So:

• singular: Der Fahrradständer hält das Fahrrad.
• plural: Die Fahrradständer halten die Fahrräder.

Notice:

• Fahrradständer stays the same in the plural
• Fahrrad changes to Fahrräder with an umlaut

Yes. That would mean A bike stand holds a bicycle.

Compare:

• Der Fahrradständer hält das Fahrrad. = The bike stand holds the bicycle.
• Ein Fahrradständer hält ein Fahrrad. = A bike stand holds a bicycle.

So the difference is mainly:

• der / das = specific, known thing
• ein / ein = non-specific thing

Both are grammatically correct.