Ég vildi óska að ég hefði meiri tíma.

Because Icelandic uses past forms here to express something unreal, hypothetical, or contrary to the current situation.

So:

• vildi is the past form of vilja but in this kind of sentence it does not simply mean a past action.
• hefði is the past subjunctive of hafa and shows that the speaker is talking about something that is not actually the case now.

This is very similar to English:

• I wish I had more time

English also uses had, which looks past, even though the meaning is about the present.

Vildi óska works as an idiomatic way to say wish.

Word for word, it looks something like:

• ég = I
• vildi = wanted / would want
• óska = wish

But you should not translate it too literally. In this sentence, Ég vildi óska að... is best understood as:

• I wish that...
• or simply I wish...

So the whole sentence means I wish I had more time.

Because hefði is the form needed for an unreal wish.

Compare:

• Ég hef meiri tíma = I have more time
• að ég hefði meiri tíma = that I had more time / if I had more time

In the sentence you gave, the speaker does not actually have enough time. That is why Icelandic uses the subjunctive form hefði instead of the normal present-tense indicative forms hef or hefur.

Að introduces the subordinate clause, like that in English.

So:

• Ég vildi óska = I wish
• að ég hefði meiri tíma = that I had more time

In natural English, that is often omitted, but in Icelandic að is very normal here.

Because there are two clauses, and each clause has its own subject.

• Main clause: Ég vildi óska
• Subordinate clause: að ég hefði meiri tíma

So the second ég belongs to the second clause. English does the same thing if you say the full version:

• I wish that I had more time

There are two things going on:

1. tíma is in the accusative
2. meiri agrees with tíma

The verb hafa takes a direct object, and that object is in the accusative case. The noun tími in the nominative becomes tíma in the accusative.

So:

• tími = time, as a subject form
• tíma = time, as an object form

And meiri is the comparative form meaning more, agreeing with masculine singular tíma.

So the phrase meiri tíma means more time.

Meiri is the comparative form of mikill, which often means much, big, or great, depending on context.

Here, meiri means more.

So:

• mikill tími = much/a lot of time
• meiri tími / meiri tíma = more time

In this sentence, because the noun is the object of the verb, you get meiri tíma.

No. Óska can be used in more than one way.

It can be followed by:

• a noun phrase
• or a clause with að

In your sentence, it is followed by a clause:

• að ég hefði meiri tíma

That clause tells us what the wish is.

So this structure is completely normal.

A fairly literal gloss would be:

• Ég = I
• vildi óska = wished / would wish
• að = that
• ég hefði = I had
• meiri tíma = more time

So a literal-ish version is:

• I would wish that I had more time

But the natural English translation is simply:

• I wish I had more time

Then you would normally use hefði haft instead of just hefði.

For example:

• Ég vildi óska að ég hefði haft meiri tíma.

That means:

• I wish I had had more time
• or more naturally, I wish I’d had more time

So:

• hefði meiri tíma = wish about the present situation
• hefði haft meiri tíma = wish about a past situation