Because cuesta is a feminine singular noun, so it takes the feminine article la.
Spanish uses ser and estar differently, and this is a very common learner question.
Here, es is used because larga describes a more inherent characteristic of the slope: its length. It is being presented as part of what the slope is like.
Using está would sound unusual here, because length is not normally thought of as a temporary state.
Because muy means very, and in Spanish it normally goes before adjectives and adverbs.
So:
You would not normally put it after the adjective.
No, Cuesta es muy larga is not correct here.
You need la because cuesta is being used as a noun meaning the slope / the hill. In this sentence, it refers to a specific slope or hill, so the definite article is natural.
Without the article, it would not work as a normal sentence.
The standard, neutral word order is:
This is the most natural way to say it.
Spanish word order can sometimes change for emphasis, but beginners should stick to the normal pattern:
So here:
Normally, no.
Even though English uses is for both ser and estar, Spanish distinguishes them. For physical characteristics like long, short, big, and small, Spanish usually uses ser.
So the correct sentence is:
Using estar with larga would sound unnatural in most ordinary contexts.
Yes, sometimes, depending on context.
Cuesta often refers to an upward slope, an incline, or a hill section of a road or path. In everyday English, that may be translated as:
So if the meaning shown to the learner is The hill is very long, that can still be fine in context. Just remember that cuesta often emphasizes the sloping/uphill part, not a hill as a landform in the broadest sense.
No, muy is used with adjectives and adverbs, not directly with nouns.
So these are correct:
But with nouns, Spanish usually uses mucho / mucha / muchos / muchas instead:
In your sentence, muy is correct because it modifies the adjective larga.