Hoc opus mihi grave est, sed id finire volo.

Because opus is a neuter noun. The demonstrative hic, haec, hoc must agree with the noun it modifies in gender, number, and case.

• opus = neuter singular nominative
• so this work / this task = hoc opus

If the noun were masculine, you would expect hic; if feminine, haec.

Opus is nominative singular here, because it is the subject of est.

The basic structure is:

• Hoc opus = the subject
• grave = predicate adjective
• est = is

So literally the clause is something like This work is burdensome.

Because grave must agree with opus, which is neuter singular.

The adjective gravis, grave has these nominative singular forms:

• masculine/feminine: gravis
• neuter: grave

Since opus is neuter, Latin uses grave.

Here mihi means to me or for me. Latin often uses the dative with adjectives to show the person affected.

So:

• Hoc opus mihi grave est
  = This task is მძიმე to me / burdensome for me
  more naturally, This task is hard for me

This is a very common Latin pattern: something is pleasant, useful, easy, difficult, harmful, etc. to someone.

Not in this construction.

• me is accusative or ablative
• mihi is dative

Since grave est here takes a person in the dative, mihi is the correct form.

So Latin says:

• mihi grave est = it is hard for me

not

• me grave est

Id is a pronoun meaning it or that. It refers back to hoc opus.

So:

• hoc opus = this task
• id = it, meaning that same task

Latin often uses a demonstrative pronoun like id where English would simply use it.

Latin could often omit id if the object were obvious, so finire volo would be possible in many contexts.

But id is included here to make the reference explicit:

• id = it
• finire volo = I want to finish

So id finire volo means I want to finish it.

Because it is the direct object of finire.

Ask: finish what?
Answer: it = id

So id is in the accusative singular neuter.

Because volo is followed by an infinitive to express want to do something.

This is a standard Latin construction:

• volo ambulare = I want to walk
• volo discere = I want to learn
• volo finire = I want to finish

So in this sentence:

• id finire volo = I want to finish it

Latin word order is much more flexible than English word order. A verb often comes near the end of the clause, especially in straightforward prose.

So:

• id finire volo
• literally: it to finish I want

But in natural English: I want to finish it

Putting volo at the end is completely normal Latin style.

They do different jobs.

• hoc is an adjective modifying opus: this task
• id is a pronoun standing by itself: it

So the sentence moves from naming the thing to referring back to it:

• Hoc opus = this task
• id = it

That is a very natural Latin way to write.

It is the same Latin word historically, but in ordinary Latin it often just means work, task, or piece of work. It does not only mean a grand artistic work.

So in this sentence, opus likely means something like:

• task
• job
• piece of work
• project

depending on context.

Yes. Latin often uses sum with an adjective to describe how something is for someone:

• grave est mihi = it is hard for me
• facile est mihi = it is easy for me
• utile est mihi = it is useful for me

So grave est is a very normal pattern.

Yes. Latin allows several word orders without changing the basic meaning, though the emphasis may change.

For example, you could see things like:

• Mihi hoc opus grave est, sed id finire volo.
• Hoc opus grave mihi est, sed id finire volo.

The version given is clear and natural. The first clause especially keeps a common pattern: subject + dative + predicate + verb.

It has two clauses joined by sed:

1. Hoc opus mihi grave est

   • hoc opus = subject
   • mihi = dative, for me / to me
   • grave = predicate adjective
   • est = verb

2. sed id finire volo

   • sed = but
   • id = direct object, it
   • finire = infinitive, to finish
   • volo = I want

So the grammar is very compact, but each part has a clear role.

Volo is first person singular present active indicative of velle, meaning to want.

So volo = I want.

It is an irregular verb, and some common forms are:

• volo = I want
• vis = you want
• vult = he/she/it wants
• volumus = we want
• vultis = you all want
• volunt = they want

Because the ending of volo already tells you the subject is I.

In Latin, subject pronouns are often omitted unless they are needed for emphasis or contrast.

So:

• volo already means I want

If Latin added ego, it would usually be for emphasis:

• ego volo = I want

But here plain volo is enough.