Mér finnst ókurteist að tala hátt í símanum á fundi.

Because finnast in this meaning does not take a normal nominative subject like English I.

• mér is the dative form of ég.
• finnst is the 3rd person singular present of finnast.

So Mér finnst ... literally means something like To me, it seems / feels / is found, but in natural English it usually means I think, I find, or It seems to me.

This is a very common Icelandic pattern:

• Mér finnst þetta gott. = I think this is good.
• Henni finnst gaman hér. = She likes it here / She finds it fun here.

So the dative mér is completely normal here.

Here finnst means seems, feels, or is considered by me.

In practice, Mér finnst ókurteist ... is a very common way to say:

• I think it is rude ...
• I find it rude ...

So it is not about physically finding something. It expresses a personal judgment or opinion.

Because the thing being judged is the whole action að tala hátt í símanum á fundi.

In Icelandic, when an adjective refers to:

• an action,
• an idea,
• a clause,
• or something abstract,

it is very often put in the neuter singular.

So:

• ókurteis = rude
• ókurteist = neuter singular form of ókurteis

The sentence is basically treating to speak loudly on the phone during a meeting as an abstract thing, and that is why the neuter form is used.

Compare:

• Þetta er ókurteist. = This is rude.
• Að koma of seint er ókurteist. = To arrive too late is rude.

að tala is the infinitive, meaning to speak or to talk.

The whole phrase

• að tala hátt í símanum á fundi

means

• to speak loudly on the phone at a meeting

This infinitive phrase is the thing being evaluated as rude.

So the structure is roughly:

• Mér finnst [ókurteist] [að tala hátt í símanum á fundi].
• I find [it rude] [to speak loudly on the phone at a meeting].

Because hátt is being used as an adverb here, meaning loudly.

The adjective is:

• hár = high, loud

But Icelandic often uses the neuter singular form of an adjective as an adverb.

So:

• hátt = loudly
• lágt = quietly / softly / low
• vel is irregular, but many others follow this pattern

In this sentence:

• tala hátt = speak loudly

So hátt is not describing a noun. It is describing how the speaking is done.

í símanum is dative singular of sími with the definite article attached.

Breakdown:

• sími = phone
• símanum = the phone, dative singular

The preposition í can take either:

• accusative for motion into
• dative for location or a non-motion situation

Here there is no movement into anything. It is the idiomatic expression for speaking on the phone / into the phone, so the dative is used:

• í símanum

Also, Icelandic often uses the definite form in places where English might simply say on the phone.

Because á fundi means at a meeting in a general, non-specific sense.

• á fundi = at a meeting
• á fundinum = at the meeting

So in your sentence, the meaning is general:

• speaking loudly on the phone during a meeting

If you were talking about one specific meeting already known in the conversation, you could say:

• Mér finnst ókurteist að tala hátt í símanum á fundinum.

Also, á here takes the dative because it refers to being at an event or location, not motion onto something.

In a sense, yes.

English often says:

• I think it is rude to speak loudly on the phone at a meeting.

Icelandic can also say that with það:

• Mér finnst það ókurteist að tala hátt í símanum á fundi.

But Icelandic very often leaves that það out when the meaning is clear, especially in sentences like this.

So your sentence is completely natural. You can think of it as:

• Mér finnst (það) ókurteist að tala hátt í símanum á fundi.

Yes, but the version you have is very natural.

Your sentence:

• Mér finnst ókurteist að tala hátt í símanum á fundi.

is a common Icelandic way to present the opinion first and then the action.

You may also see:

• Mér finnst það ókurteist að tala hátt í símanum á fundi.

That version is also very natural and slightly fuller because it includes það.

A version like:

• Að tala hátt í símanum á fundi er ókurteist.

also works, but now the infinitive phrase comes first and becomes the grammatical subject:

• Speaking loudly on the phone at a meeting is rude.

So the meaning is similar, but the structure is different.

They are similar, but Mér finnst is much more common in everyday modern Icelandic.

Both can express personal opinion:

• Mér finnst þetta skrítið. = I think this is strange.
• Mér þykir þetta skrítið. = similar meaning, but often sounds more formal, literary, or old-fashioned in many contexts

So for ordinary conversation, Mér finnst is usually the safest choice.

A useful way to see it is:

• Mér = to me
• finnst = seems / I find
• ókurteist = rude
• að tala = to speak
• hátt = loudly
• í símanum = on the phone
• á fundi = at a meeting

So the pattern is:

• dative experiencer + finnast + neuter adjective + infinitive phrase

This is a very common Icelandic structure for giving opinions about actions, for example:

• Mér finnst erfitt að vakna snemma. = I find it hard to wake up early.
• Mér finnst skemmtilegt að læra íslensku. = I think learning Icelandic is fun.
• Mér finnst leiðinlegt að bíða. = I find waiting boring.