Tämä sääntö koskee kaikkia.

• tämä = this. Here it modifies sääntö, so it works like a determiner: this rule.
• sääntö = rule. This is the subject of the sentence.
• koskee = concerns / applies to. This is the 3rd person singular present form of koskea.
• kaikkia = everyone / all people / all of them, depending on context. Grammatically, it is in the partitive plural.

So the structure is basically:

[This rule] [applies to] [everyone].

Because the verb koskea in the meaning concern / apply to normally takes its object in the partitive.

So:

• Tämä sääntö koskee kaikkia. = This rule applies to everyone.
• Asia koskee minua. = The matter concerns me.
• Se koskee meitä kaikkia. = It concerns all of us.

This is something English speakers usually just have to learn together with the verb:

• koskea + partitive = to concern, apply to

So it is not random; it is part of the verb’s grammar.

They are in the nominative singular.

• tämä = nominative singular of this
• sääntö = nominative singular of rule

That makes sense because tämä sääntö is the subject of the sentence.

If the phrase changed role in the sentence, the forms could change too. For example:

• tämän säännön = of this rule / this rule’s / this rule in some object uses
• tässä säännössä = in this rule

But in your sentence, the basic subject form is used.

Because the subject is singular:

• tämä sääntö = this rule → singular

So the verb must also be singular:

• koskee = 3rd person singular present

If the subject were plural, the verb would be plural too:

• Nämä säännöt koskevat kaikkia. = These rules apply to everyone.

So the agreement is:

• singular subject → koskee
• plural subject → koskevat

No. Koskea has more than one meaning, and the structure can change depending on the meaning.

Common meanings include:

• to concern / apply to
  • Tämä sääntö koskee kaikkia.
• to touch
  • Älä koske siihen! = Don’t touch it!

That is important because Finnish verbs often have different patterns with different meanings. So when learning a verb, it helps to learn:

• the meaning
• the case or form it requires

In this sentence, koskea clearly means to concern / apply to.

It depends on context.

kaikkia literally means something like all (of them) in the partitive plural. In real sentences, the exact English translation depends on what is being talked about.

Here, with a rule, the natural meaning is usually:

• everyone
• all people
• everybody

But in another context it could refer to things:

• Se koskee kaikkia laitteita. = It applies to all devices.

So kaikkia itself does not always mean only people; context tells you what all refers to.

Yes. That would be more explicit.

• Tämä sääntö koskee kaikkia. = This rule applies to everyone.
• Tämä sääntö koskee kaikkia ihmisiä. = This rule applies to all people.

In many situations, just kaikkia is enough because the listener can understand the missing noun from context.

This is common in Finnish: the noun can be left out if it is obvious.

The neutral word order is:

• Tämä sääntö koskee kaikkia.

But Finnish word order is fairly flexible, and changing it often changes the emphasis rather than the basic meaning.

For example:

• Kaikkia tämä sääntö koskee.
  This emphasizes everyone.
• Tätä sääntöä koskee... would be different grammar and a different meaning, so you cannot just move words around without checking the forms.

So yes, the words can move, but the basic version you have is the most neutral and natural one.

Because Finnish normally does not use articles like English the and a/an.

So:

• sääntö can mean a rule or the rule
• tämä sääntö means this rule, which is already specific

Finnish usually shows definiteness through:

• context
• word order
• demonstratives like tämä = this, tuo = that
• possessive structures, if needed

So English learners often look for an article, but Finnish simply does not need one here.

A rough pronunciation guide for an English speaker:

• Tämä ≈ TEH-mae
• sääntö ≈ SAEN-tuh
• koskee ≈ KOS-keh
• kaikkia ≈ KAIK-kee-ah

A few important points:

• ä is not the same as English a. It is closer to the vowel in some pronunciations of cat, but cleaner and shorter.
• ö has no exact English equivalent. It is somewhat like the vowel in French deux or German schön if you know those.
• Double vowels are long:
  • sää
  • kee
• Double consonants are also pronounced more strongly in Finnish, though this sentence does not have many striking examples of that.

Finnish pronunciation is usually quite regular, so once you know the sounds, reading becomes much easier.

If you want to say These rules apply to everyone, you would say:

• Nämä säännöt koskevat kaikkia.

Changes:

• tämä → nämä = this → these
• sääntö → säännöt = rule → rules
• koskee → koskevat = applies → apply

kaikkia stays the same, because it is still the partitive plural object required by koskea.

The dictionary form is koskea.

The form koskee is the 3rd person singular present.

Many Finnish verbs of this type work like this:

• dictionary form: lukea → 3rd person singular: lukee
• dictionary form: hakea → 3rd person singular: hakee
• dictionary form: koskea → 3rd person singular: koskee

So the final vowel is lengthened in this form.

That means:

• minä kosken = I concern / touch
• sinä kosket
• hän/se koskee

In your sentence, the subject is not a person but this rule, so Finnish uses the same 3rd person singular form: koskee.