Mekanikken påvirker demperen.

Because both nouns are in the definite singular form.

In Norwegian, the idea of the is usually added to the end of the noun:

• mekanikk → mekanikken = the mechanics / the mechanism
• demper → demperen = the damper

So instead of a separate word like English the, Norwegian often uses a suffix.

For simple definite nouns, Norwegian normally attaches the definite article to the noun itself.

So:

• English: the damper
• Norwegian: demperen

You only often see an extra word like den/det/de when there is an adjective:

• demperen = the damper
• den store demperen = the big damper

This is a very common Norwegian pattern.

Because these nouns are common gender nouns in Bokmål.

A quick rule:

• en noun → definite singular usually ends in -en
• et noun → definite singular usually ends in -et

Examples:

• en demper → demperen
• et hus → huset

So demperen tells you that demper is not a neuter noun.

Påvirker is the present tense of the verb påvirke.

• å påvirke = to affect / influence
• påvirker = affects / is affecting

In a sentence like this, Norwegian uses the present tense very simply:

• Mekanikken påvirker demperen.

That can correspond to English affects or sometimes is affecting, depending on context.

No. Norwegian verbs do not change for person the way English verbs sometimes do.

Compare:

• jeg påvirker
• du påvirker
• han påvirker
• de påvirker

It stays påvirker in all of these. That is much simpler than English.

In a basic Norwegian statement, the usual order is:

Subject + Verb + Object

So in:

Mekanikken påvirker demperen

• mekanikken = subject
• påvirker = verb
• demperen = object

So mekanikken is doing the affecting, and demperen is being affected.

Norwegian usually relies much more on word order than on case endings.

Yes. Mekanikk is grammatically a singular noun in Norwegian.

So:

• mekanikk = mechanics / mechanics as a field / mechanism-related principle
• mekanikken = the mechanics

If you mean a mechanic as a person, that is a different word:

• en mekaniker = a mechanic
• mekanikeren = the mechanic

That is a very useful distinction to remember.

That depends on context. Demper is a technical word that can refer to different kinds of damping or muffling devices.

Depending on the situation, it might mean something like:

• damper
• shock absorber
• muffler
• silencer

So the exact English word depends on what kind of system you are talking about. The Norwegian grammar stays the same either way.

A few useful pronunciation points:

• å in på sounds roughly like the vowel in paw
• y in påvirker is a sound English does not really have; it is similar to French u or German ü
• the stress is on the first syllable: PÅ-virker

A rough learner-friendly guide might be:

• påvirker ≈ PAW-vyr-ker

Not perfect, but good enough as a starting point.

Yes, but the normal pattern here is the safest one:

Subject + Verb + Object

So:

• Mekanikken påvirker demperen.

If you move things around, you may change the emphasis or even the meaning:

• Demperen påvirker mekanikken.
  Now the damper is the subject, so the meaning changes.

Also remember that Norwegian usually keeps the finite verb in the second position:

• I dag påvirker mekanikken demperen.

So the basic sentence you have is a very standard Norwegian word order pattern.