La résolution est claire.

Because résolution is a feminine noun in French. French nouns have grammatical gender, so you have to use the matching article:

• la résolution = feminine singular
• le would be for a masculine singular noun

This is something you usually have to learn with the noun itself.

Because French adjectives usually agree with the noun they describe in gender and number.

Here, résolution is feminine singular, so the adjective must also be feminine singular:

• masculine singular: clair
• feminine singular: claire
• masculine plural: clairs
• feminine plural: claires

So La résolution est claire uses claire because résolution is feminine.

Est is the third-person singular present form of être, which means to be.

So the structure is:

• La résolution = the subject
• est = is
• claire = the adjective

It works very much like English The resolution is clear.

Because the subject is already stated: La résolution.

In English, you might sometimes say It is clear, but here French is directly saying The resolution is clear, so no extra subject pronoun is needed.

In this sentence, claire comes after est, not directly after the noun, because it is part of the pattern:

subject + être + adjective

So this is not really about adjective position inside a noun phrase. It is a normal predicate adjective structure:

• La résolution est claire
• literally: The resolution is clear

If you put the adjective directly with the noun, you would get:

• une résolution claire = a clear resolution

There too, claire normally comes after the noun, because clair/claire is usually a post-nominal adjective in French.

Yes, but it is not exactly the same structure.

• La résolution est claire directly describes the resolution
• C’est clair means That’s clear or It’s clear, and often comments on the whole situation or statement

So if you want to describe the noun résolution, the sentence you have is more precise.

La is the definite article, so it refers to a specific resolution that is already known or identifiable in context.

• La résolution est claire = The resolution is clear
• Une résolution est claire = A resolution is clear

The second version is grammatically possible, but it sounds more general or less natural unless the context specifically calls for a resolution rather than the resolution.

A careful pronunciation is approximately:

[la ʁe.zɔ.ly.sjɔ̃ ɛ klɛʁ]

A rough English-friendly guide could be:

la ray-zoh-loo-syon eh clair

A few useful points:

• résolution has the French r, not an English r
• the ending -tion sounds like syon
• est is pronounced like eh
• claire sounds a bit like English Claire, but with a French r

Often yes, but context matters.

French résolution can refer to several things, including:

• a decision or determination
• a formal resolution
• the resolution of an image or screen
• the solving of a problem

So the word is close to English resolution, but you still need context to know exactly which sense is meant.

Yes. Like English clear, clair/claire can have a few related meanings depending on context, such as:

• easy to understand
• obvious
• unambiguous
• bright/light in some contexts

In this sentence, it is describing résolution as understandable or well-defined, depending on the context already given.