Ég tæmi glasið og fylli það með vatni.

They are the 1st person singular present tense forms of the verbs tæma and fylla.

• að tæma = to empty
• að fylla = to fill
• ég tæmi = I empty / I am emptying
• ég fylli = I fill / I am filling

So the -i ending here matches the subject ég in the present tense.

The dictionary forms are:

• að tæma = to empty
• að fylla = to fill

In Icelandic, dictionaries normally list verbs in the infinitive with að.

Because glasið means the glass, while glas means a glass or just glass depending on context.

Icelandic usually adds the definite article to the end of the noun instead of putting a separate word in front of it.

• glas = glass
• glasið = the glass

So -ið here is the suffixed definite article.

It is the direct object of tæmi, so it is in the accusative.

However, with the neuter noun glas, the nominative and accusative forms are the same in the singular definite form, so you do not see a visible difference here.

So grammatically it is accusative, even though it looks the same as nominative.

Það means it, and it refers back to glasið.

Instead of repeating the noun, Icelandic naturally uses a pronoun here:

• Ég tæmi glasið og fylli það með vatni.

That works just like English I empty the glass and fill it with water.

Because glas is a neuter singular noun, and the pronoun has to match it.

• glas = neuter singular
• það = it for a neuter singular noun

Also, það is the object of fylli, so it is functioning as an object here. Conveniently, the neuter singular form það looks the same in nominative and accusative.

Because the preposition með normally takes the dative case when it means with.

The noun vatn has these relevant forms:

• vatn = nominative/accusative
• vatni = dative

So after með, you get:

• með vatni = with water

Here it tells you what the glass is being filled with.

So fylli það með vatni means fill it with water.

This is a very common Icelandic pattern:

• fylla eitthvað með einhverju
  = to fill something with something

So:

• eitthvað = the thing being filled
• einhverju = what you fill it with, in the dative after með

Because both verbs have the same subject, ég.

So Icelandic can say:

• Ég tæmi glasið og fylli það með vatni.

This is like English:

• I empty the glass and fill it with water.

You could say og ég fylli það með vatni, but that sounds more emphatic or more separate. Leaving out the second ég is completely normal.

It can mean either, depending on context.

The forms tæmi and fylli are present tense, and Icelandic often uses the plain present in places where English might use either:

• I empty the glass and fill it with water
• I am emptying the glass and filling it with water

So the exact time sense comes from the situation, not just from the verb form.

Yes, you could say:

• Ég tæmi glasið og fylli glasið með vatni.

This is grammatically possible, but it sounds more repetitive. Using það is more natural once glasið has already been mentioned.

Yes. The structure is very straightforward:

• Ég = subject
• tæmi = verb
• glasið = object
• og = and
• fylli = second verb
• það = object
• með vatni = prepositional phrase

So the sentence follows a normal and natural Icelandic pattern.