Ég keypti hvíta málningu og nýjan pensil í búðinni á horninu.

Keypti is the past tense of kaupa, meaning bought.

So:

• kaupa = to buy
• ég keypti = I bought

This is the normal past-tense form you need in this sentence. As in many Icelandic verbs, the past tense is not formed in a way that always looks obvious to an English speaker, so it is best learned together with the infinitive.

Because they are direct objects of keypti, and the verb kaupa takes the accusative case for what is bought.

Dictionary forms:

• málning = paint
• pensill = brush

Accusative singular forms here:

• málningu
• pensil

So the sentence uses object forms, not nominative forms.

Because Icelandic adjectives must agree with the noun they describe in:

• gender
• number
• case

Here:

• málningu is feminine singular accusative
  → hvíta
• pensil is masculine singular accusative
  → nýjan

So the different adjective endings are not random. They match the different nouns.

They are strong adjective forms.

A simple rule is:

• use strong adjective forms with indefinite nouns
• use weak adjective forms with definite nouns or with words like demonstratives

In this sentence:

• hvíta málningu = white paint
• nýjan pensil = a new brush

These are indefinite, so strong forms are used.

Compare:

• hvíta málningu = white paint
• hvítu málninguna = the white paint

Because Icelandic normally has no indefinite article.

So where English says:

• a new brush

Icelandic simply says:

• nýjan pensil

The meaning of a/an is understood from the fact that the noun is indefinite.

Because í changes case depending on whether it means location or movement.

• í + dative = in, inside a place
• í + accusative = into a place

Here the meaning is location:

• í búðinni = in the shop

The speaker bought the items while in the shop, not moving into the shop.

Compare:

• Ég var í búðinni. = I was in the shop.
• Ég fór í búðina. = I went into the shop.

For the same general reason: á also changes case depending on meaning.

• á + dative = location
• á + accusative = movement onto/to

Here it means location:

• á horninu = on the corner

This is the normal way to say on the corner when describing where a building or shop is. It is an idiomatic location phrase, not a literal idea of something sitting on top of a corner.

In Icelandic, the definite article is usually added to the end of the noun instead of being a separate word.

So:

• búð = shop
• búðin = the shop
• búðinni = in the shop / to the shop, depending on case and context

And:

• horn = corner
• hornið = the corner
• horninu = on the corner / at the corner, in dative here

So the is built into the noun itself.

Because both are controlled by prepositions showing location:

• í búðinni → í
  • dative for location
• á horninu → á
  • dative for location

This is a very common Icelandic pattern. Many prepositions use one case for location and another for movement/direction.

Yes. Og means and, and it joins two direct objects of the same verb:

• hvíta málningu
• nýjan pensil

Both are things that were bought.

So the structure is:

• Ég keypti
  • object 1 + og
    • object 2

Each noun phrase keeps its own adjective and its own correct agreement.

Yes. Málning is often used as a mass noun, much like English paint.

So:

• hvíta málningu = white paint

This does not have to mean one single can or one clearly countable item. It can mean the substance in general, just like English I bought white paint.

It can move, but Icelandic has a strong verb-second tendency in main clauses.

The sentence as given has a very normal order:

• Ég keypti hvíta málningu og nýjan pensil í búðinni á horninu.

You could also front the place phrase:

• Í búðinni á horninu keypti ég hvíta málningu og nýjan pensil.

Notice that the finite verb keypti still comes early in the clause. That is a very important Icelandic word-order pattern.