Ég hoppa ekki eins hátt og hún, því trampólínið er blautt eftir rigninguna.

Yes, að hoppa is the infinitive, but the 1st person singular present tense is also hoppa.

So the pattern is:

• að hoppa = to jump
• ég hoppa = I jump
• þú hoppar = you jump
• hún hoppar = she jumps

This is very common with Icelandic weak verbs. So Ég hoppa ekki... is completely normal and means I do not jump...

Eins ... og is the standard pattern for an equal comparison, meaning as ... as.

So:

• eins hátt og hún = as high as she does

Icelandic uses:

• eins + adjective/adverb + og = as ... as
• comparative + en = more/less ... than

For example:

• eins hátt og hún = as high as she does
• hærra en hún = higher than she is / than she does

So og is correct here because this is an as ... as comparison, not a more ... than comparison.

Because hátt is functioning as an adverb, not an adjective.

The sentence is describing how someone jumps, not describing the person directly. In English, we say jump high, not jump tall. Icelandic does the same kind of thing.

• hár = high / tall as an adjective
• hátt = high as an adverb

With many Icelandic adjectives, the adverb is the neuter singular form of the adjective. So:

• hár → hátt

That is why Ég hoppa ekki eins hátt... means I do not jump as high...

Because hún is understood as the subject of an omitted clause:

• eins hátt og hún [hoppar]

So the full idea is as high as she jumps. Since hún is the subject of that understood verb, it stays in the nominative case.

This is similar to very formal English as high as she rather than colloquial as high as her. In Icelandic, using hún here is the normal form for learners to use.

Because Icelandic often leaves out a repeated verb when it is obvious from the context.

So:

• Ég hoppa ekki eins hátt og hún
  really means
• Ég hoppa ekki eins hátt og hún hoppar

The second hoppar is omitted because it would be repetitive and the meaning is already clear. English does something similar:

• I don’t jump as high as she does

The does is often needed in English, but Icelandic can simply stop at hún.

In a simple main clause, ekki usually comes after the finite verb.

So:

• Ég hoppa ekki = I do not jump

This is the normal placement of negation in Icelandic.

Compare:

• Ég er ekki þreytt(ur) = I am not tired
• Ég kann ekki íslensku = I do not know Icelandic

If there is an auxiliary verb, ekki usually follows that finite auxiliary:

• Ég hef ekki hoppað = I have not jumped

Here því means because.

So:

• ..., því trampólínið er blautt ... = ..., because the trampoline is wet ...

Yes, you could also say af því að, which is another very common way to say because.

For example:

• Ég hoppa ekki eins hátt og hún, af því að trampólínið er blautt eftir rigninguna.

Both are natural. Því can sound a bit more compact or slightly more written, but it is very common and completely normal.

Because Icelandic usually puts the definite article onto the end of the noun.

So:

• trampólín = trampoline / a trampoline
• trampólínið = the trampoline

The ending -ið is the definite article here for a neuter singular noun.

This is one of the big differences from English. Instead of a separate word like the, Icelandic often attaches it:

• hús = house
• húsið = the house

Blautt is the form of blautur that agrees with trampólínið.

Since trampólínið is:

• neuter
• singular
• nominative (the subject)

the adjective must also be neuter singular nominative:

• blautur = wet
• blautt = wet, neuter singular form

This is why the sentence says:

• trampólínið er blautt = the trampoline is wet

The double t is just part of how this adjective changes in that form. Icelandic adjectives often change quite a lot to match gender, number, and case.

Here eftir means after, and rigninguna is in the accusative singular definite.

So:

• rigning = rain
• rigningin = the rain, nominative
• rigninguna = the rain, accusative

In this sentence:

• eftir rigninguna = after the rain

That accusative form is required by eftir in this time expression.

The definite article is used because it refers to a specific rain event: the rain that happened before the trampoline became wet.