Jeg er enig i dit forslag.

Because forslag is a neuter noun in Danish, and neuter nouns take dit for your.

• en stol → din stol
• et forslag → dit forslag

So the noun’s gender controls the form of the possessive.

Yes. The noun is:

• et forslag = a suggestion / a proposal

Since it is an et-word, you get:

• mit forslag = my suggestion
• dit forslag = your suggestion
• vores forslag = our suggestion

This is one of the reasons it is useful to learn Danish nouns together with en or et.

Enig is an adjective. It means in agreement or agreed.

In this sentence, jeg er enig literally means something like I am in agreement.

It is very commonly used with være:

• Jeg er enig = I agree / I am in agreement
• Hun er enig = She agrees / She is in agreement

Because Danish normally uses enig i when you agree with something, such as:

• an idea
• a plan
• a suggestion
• a statement

So:

• Jeg er enig i dit forslag = I agree with your suggestion/proposal

You can think of enig i as a fixed pattern that learners should memorize.

Yes, but it means something slightly different.

• enig i noget = agree with something
• enig med nogen = agree with someone

Examples:

• Jeg er enig i dit forslag. = I agree with your suggestion.
• Jeg er enig med dig. = I agree with you.

You can also combine both:

• Jeg er enig med dig i dit forslag.

That means I agree with you about your suggestion, though in everyday speech people often choose the simpler version that fits what they want to emphasize.

It actually can change in other contexts, but not here.

With jeg, the adjective stays in its basic form:

• Jeg er enig
• Du er enig
• Han er enig

But in the plural, it becomes enige:

• Vi er enige
• De er enige

So if the subject changes, the adjective may change too.

Yes, it is completely natural and idiomatic.

It sounds like standard, correct Danish. Depending on context, a Dane might also say:

• Jeg er enig. = I agree.
• Jeg synes, dit forslag er godt. = I think your suggestion is good.
• Det er jeg enig i. = I agree with that.

But your sentence is a very normal way to express agreement with a suggestion.

Both can sometimes translate as idea or suggestion, but they are not always identical.

• forslag usually means a proposal or suggestion, often something being put forward for consideration
• idé means an idea

So:

• dit forslag = your proposal / your suggestion
• din idé = your idea

If someone has already suggested a concrete course of action, forslag is often the better word.

Normally, no. In this sentence, om would not be the standard preposition.

The usual choice is:

• enig i noget
• enig med nogen

So the correct sentence is:

• Jeg er enig i dit forslag.

Prepositions in Danish often do not match English exactly, so this is a good expression to learn as a set phrase.

A rough learner-friendly guide would be:

• jeg ≈ yai or yigh depending on accent
• er ≈ a soft air
• enig ≈ ee-ni
• i = ee
• dit ≈ di or a very soft dit
• forslag ≈ foh-slay

A few important points:

• j in jeg is not like English j in job; it is more like y
• final consonants are often softer than English learners expect
• Danish pronunciation varies a lot by region and can be much less phonetic than the spelling suggests

If you want, the best approach is to listen to native audio and repeat the whole chunk:

Jeg er enig i dit forslag.

Yes. In a yes/no question, the verb comes before the subject:

• Er du enig i mit forslag? = Do you agree with my suggestion?

This is a very common Danish pattern:

• statement: Du er enig i mit forslag.
• question: Er du enig i mit forslag?

So Danish often uses verb before subject to form questions.

Yes, if the context already makes it clear which proposal you mean.

• Jeg er enig i dit forslag. = I agree with your proposal.
• Jeg er enig i forslaget. = I agree with the proposal.

The difference is:

• dit forslag points specifically to your proposal
• forslaget means the proposal

Both are correct, but they do not mean exactly the same thing.

It is neutral and works well in both formal and informal contexts.

You could say it:

• in a conversation with a friend
• in a meeting
• in an email
• in a classroom discussion

If you want to sound a little more formal, you might say:

• Jeg er enig i Deres forslag.

Here Deres is the formal your, though in modern Danish this is much less common than it used to be.