Ég skil skoðunina hennar, þó að ég sé ekki alveg sammála.

Because skilja takes a direct object, and that object is normally in the accusative.

Here the noun is:

• skoðun = opinion/view, feminine singular
• skoðunina = the opinion, accusative singular definite

So Ég skil skoðunina hennar literally has the opinion as the thing being understood.

That is normal Icelandic word order for this kind of possessive.

The third-person possessive forms:

• hans = his
• hennar = her
• þeirra = their

usually follow the noun in ordinary Icelandic:

• bókin hennar = her book
• skoðunin hennar / skoðunina hennar = her opinion

So even though English says her opinion, Icelandic commonly says the equivalent of the opinion her.

Because Icelandic often allows — and very commonly uses — both the definite article and a possessive together.

So:

• skoðunina hennar is perfectly normal Icelandic
• it does not sound redundant to Icelandic speakers

English usually chooses just her opinion, but Icelandic often uses the suffixed article as well when referring to a specific, identifiable thing.

Hennar is the genitive form of hún (she), and here it functions as a possessive: her.

So you can think of it as:

• hún = she
• hana = her (object)
• hennar = her / hers

In this sentence, hennar modifies skoðunina and shows whose opinion it is.

Þó að introduces a concessive subordinate clause, meaning although, even though, or though.

So the structure is:

• main clause: Ég skil skoðunina hennar
• subordinate clause: þó að ég sé ekki alveg sammála

It connects the two ideas in the sense of:

• I understand her opinion, although ...
• I understand her opinion, even though ...

Because after þó að, Icelandic very often uses the subjunctive.

• er = present indicative of vera (to be)
• sé = present subjunctive of vera

So þó að ég sé ... is the expected standard pattern here.

This is one of the common places where learners meet the Icelandic subjunctive.

Sé is the present subjunctive of vera (to be).

In this sentence it goes with ég, but the same form is also used with some other persons, so it may feel a little unusual at first.

The important thing to remember here is simply:

• ég er = I am
• þó að ég sé = although I be / although I am

In natural English we do not translate the subjunctive separately here; we just say although I am.

Because this is a subordinate clause.

Icelandic main clauses often follow the verb-second pattern, but subordinate clauses introduced by words like þó að usually do not invert the subject and verb in that way.

So after þó að, the normal order is:

• conjunction + subject + finite verb

That gives:

• þó að ég sé ...

not

• þó að sé ég ...

Literally, it means not completely in agreement.

In more natural English, it usually comes out as:

• not quite agree
• not entirely agree
• not completely agree

The word alveg often means completely, entirely, or quite, and with ekki it softens the disagreement a little:

• ekki sammála = do not agree
• ekki alveg sammála = do not quite / do not entirely agree

Sammála is used like a predicate adjective, usually after vera.

So:

• Ég er sammála = I agree
• Ég er sammála henni = I agree with her
• Ég er sammála þessu = I agree with this

In your sentence, the thing or person being agreed with is left unstated because it is clear from context: the speaker understands her opinion, but is not fully in agreement with it.

For a learner, it is useful to remember the pattern:

• vera sammála + dative

Because Icelandic often uses commas to set off subordinate clauses, especially when they come after the main clause.

So this punctuation is very natural in Icelandic:

• Ég skil skoðunina hennar, þó að ég sé ekki alveg sammála.

English punctuation is often a little lighter, but Icelandic commonly marks this boundary with a comma.

Yes, but it would not be exactly the same structure.

• en = but
• þó að = although / even though

So:

• Ég skil skoðunina hennar, en ég er ekki alveg sammála.
  = I understand her opinion, but I do not quite agree.

• Ég skil skoðunina hennar, þó að ég sé ekki alveg sammála.
  = I understand her opinion, although I do not quite agree.

The meaning is close, but þó að makes the second part a subordinate concessive clause, while en simply coordinates two main clauses.