Дружба и уважение помогают людям доверять друг другу.

Because together they form a compound subject: дружба и уважение = friendship and respect. In Russian, when two subjects are joined by и (and), the verb is usually plural.

• Дружба помогает = Friendship helps
• Уважение помогает = Respect helps
• Дружба и уважение помогают = Friendship and respect help

Because the verb помогать requires the dative case for the person being helped.

Russian asks:

• помогать кому? = to help whom?

So:

• люди = people (base plural form)
• людям = to people / for people (dative plural)

That is why the sentence has помогают людям.

The form людям comes from люди, which means people.

A useful thing to know is that люди is the plural used for человек (person). So Russian works like this:

• singular: человек = person
• plural: люди = people
• dative plural: людям = to people

This is a very common irregular pattern, so it is worth memorizing early.

Because Russian often uses this pattern:

• помогать кому-то делать что-то = to help someone do something

So here:

• помогают людям = help people
• доверять друг другу = trust each other

Together:

• помогают людям доверять друг другу = help people trust each other

This works a lot like English help someone do something.

Because доверять takes the dative case:

• доверять кому? = to trust whom?

The reciprocal expression друг другу is the form that means to each other in this dative pattern.

Compare:

• Они видят друг друга. = They see each other.
  Here видеть takes the accusative, so you get друг друга.

• Они доверяют друг другу. = They trust each other.
  Here доверять takes the dative, so you get друг другу.

So the form changes depending on the verb.

Yes, that is a good approach at first.

It means each other / one another, and it changes depending on the grammar around it. Some common patterns are:

• друг друга = each other after verbs needing the accusative
• друг другу = to each other after verbs needing the dative
• друг с другом = with each other

So for this sentence, it is best to learn:

• доверять друг другу = to trust each other

as a chunk.

Because the sentence expresses a general truth or ongoing tendency, not a single completed event.

• помогают = help / are helpful in helping
• доверять = to trust

Russian normally uses the imperfective for statements like this:

• Exercise helps people sleep better
• Friendship and respect help people trust each other

A perfective verb would suggest a single completed action, which would not fit this general statement well.

Yes, Russian word order is more flexible than English, because case endings show the grammatical roles.

The sentence as written is the most neutral and natural:

• Дружба и уважение помогают людям доверять друг другу.

Changing the order is possible, but it changes emphasis and can sound more marked or literary. For example, putting людям earlier may emphasize people more strongly.

So the main thing to remember is:

• Russian word order is flexible
• the given order is the normal, neutral one

Because Russian does not have articles like English a/an and the.

So:

• дружба can mean friendship or the friendship, depending on context
• уважение can mean respect or the respect
• людям can mean to people or to the people

In this sentence, the meaning is general, so English naturally uses bare nouns too: Friendship and respect help people trust each other.

Here is the basic breakdown:

• Дружба — nominative singular

• уважение — nominative singular
  These are the subject of the sentence.

• людям — dative plural
  This is used because помогать takes the dative.

• друг другу — reciprocal expression in the dative pattern
  This is used because доверять takes the dative.

So a good grammar map is:

• [Subject in nominative] помогают [person in dative] [infinitive phrase]

In this sentence:

• Дружба и уважение — subject
• помогают — verb
• людям — indirect object
• доверять друг другу — infinitive phrase meaning to trust each other