Salurinn er stærri en ég hélt, og sætin eru þægileg.

Because Icelandic usually adds the definite article to the end of the noun instead of using a separate word like the.

• salur = hall
• salurinn = the hall
• sæti = seat
• sætin = the seats

So this sentence is talking about a specific hall and specific seats.

Stærri is the comparative form of stór.

• stór = big / large
• stærri = bigger / larger
• stærstur = biggest / largest

So Salurinn er stærri... means The hall is bigger/larger...

This is an irregular comparison, so it is not built in a fully predictable way from stór.

Yes, en can mean but, but here it means than because it follows a comparative adjective: stærri.

So:

• stærri en... = bigger than...

The comparative adjective tells you that en is being used as than, not but.

Halda can mean hold, but it also very commonly means think, believe, or suppose in certain contexts.

For example:

• Ég held... = I think...
• Ég hélt... = I thought...

So in this sentence, ég hélt means I thought.

Because Icelandic often uses halda where English would use think in the sense of suppose or believe.

So ég hélt here is very natural Icelandic for I thought / I had thought.

Using hugsaði would sound more like I was thinking or refer more literally to the act of thinking, not necessarily to a belief or assumption.

Icelandic often leaves out information that is obvious from the context.

A fuller version could be:

Salurinn er stærri en ég hélt að hann væri.

That literally means something like The hall is bigger than I thought that it was.

But in normal Icelandic, the shorter Salurinn er stærri en ég hélt is very natural and idiomatic.

Because þægileg is a predicate adjective here: it comes after eru and describes the subject.

In Icelandic, predicate adjectives normally use the strong form, even when the noun is definite.

Compare:

• þægilegu sætin = the comfortable seats
  
  • adjective before the noun, so it takes a weak definite form
• sætin eru þægileg = the seats are comfortable
  
  • adjective after eru, so it takes a predicate/strong form

So þægileg is exactly the form you would expect here.

The dictionary form is þægilegur.

Icelandic adjectives change form to match gender, number, and case. Here the subject is sætin, which is neuter plural, so the adjective appears as þægileg.

So:

• dictionary form: þægilegur
• form used here: þægileg

Both are forms of the verb vera = to be.

• er = is
• eru = are

So:

• Salurinn er... because salurinn is singular
• sætin eru... because sætin is plural

They are all in the nominative.

• salurinn is the subject of er
• ég is the subject of hélt
• sætin is the subject of eru

That is why you see ég, not some other pronoun form: it is the subject of its own clause after en.