Мне нравится этот лак для ногтей, потому что он не слишком яркий.

Because Russian structures to like differently from English.

• Мне нравится X literally means X is pleasing to me.
• мне = to me (dative case)
• нравится = is pleasing / appeals

So in this sentence, этот лак для ногтей is the thing doing the pleasing, grammatically speaking.

By contrast, я нравлюсь means I am pleasing / someone likes me.

Because the grammatical subject is этот лак для ногтей, and the head noun is лак, which is singular.

Russian verbs agree with the subject:

• нравится = singular
• нравятся = plural

So:

• Мне нравится этот лак = I like this nail polish
• Мне нравятся эти лаки = I like these nail polishes

Even though для ногтей contains a plural noun, the main noun is still лак.

Этот means this, and it has to match лак in gender, number, and case.

Here, лак is:

• masculine
• singular
• nominative

So the correct form is этот.

Compare:

• этот лак = this polish/lacquer
• эта книга = this book
• это окно = this window
• эти лаки = these polishes

Literally, it means lacquer for nails.

Breakdown:

• лак = lacquer / polish
• для = for
• ногтей = of nails / nails (genitive plural)

So лак для ногтей is the normal Russian way to say nail polish.

Because the preposition для requires the genitive case.

The base word is ноготь = fingernail / nail.
Its genitive plural form is ногтей.

So:

• ногти = nails
• для ногтей = for nails

This is very common in Russian: after для, the following noun usually goes into the genitive.

Because Russian pronouns follow grammatical gender, not natural gender.

The noun лак is masculine, so the pronoun referring to it is он.

So:

• лак → он
• книга → она
• окно → оно

Even though English uses it, Russian chooses он, она, or оно depending on the noun’s gender.

Because яркий is an adjective describing the nail polish, while ярко is an adverb.

Here, the sentence is saying the polish is not too bright, so Russian uses the adjective agreeing with он:

• он не слишком яркий = it is not too bright

Since он is masculine singular, the adjective is also masculine singular:

• яркий

If you used ярко, that would mean brightly, which is not what the sentence needs.

In the present tense, Russian usually omits the verb to be.

So:

• он яркий literally = he/it bright
• natural English = it is bright

That is completely normal in Russian.
If you wanted past or future, forms of быть would appear:

• он был яркий = it was bright
• он будет яркий = it will be bright

It means not too bright or not overly bright.

• слишком = too / excessively
• яркий = bright
• не слишком яркий = not excessively bright

This is not a double negative. The не simply negates the idea of being too bright.

Compare:

• слишком яркий = too bright
• не слишком яркий = not too bright
• не очень яркий = not very bright

Yes, you could, but the nuance changes a little.

• не слишком яркий = not too bright, not overly bright
• не очень яркий = not very bright

The first one focuses on the idea that the color is acceptable because it is not excessive.
The second one simply says it is not very bright.

Both can work, but не слишком яркий matches the English idea of not too bright more closely.

Because потому что introduces a subordinate clause, and in standard Russian that clause is separated by a comma.

So:

• Мне нравится этот лак для ногтей, потому что он не слишком яркий.

This comma is standard and expected in normal writing.

Yes. Russian word order is fairly flexible, although the emphasis changes.

The original sentence is neutral and natural:

• Мне нравится этот лак для ногтей, потому что он не слишком яркий.

You could also say:

• Этот лак для ногтей мне нравится, потому что он не слишком яркий.

That version puts more focus on this nail polish.

So the grammar still works, but the information focus shifts a bit.

You could, but it is stronger.

• мне нравится = I like
• я люблю = I love

For everyday preferences, Russian often uses нравится.
Using люблю for an object is possible, but it sounds more emotional or emphatic.

So in this sentence, мне нравится is the more neutral and natural choice.