Med den her pensel kan jeg male ved vinduet, men med den der rulle går det hurtigere.

They mean this and that:

• den her pensel = this brush
• den der rulle = that roller

This is a very common spoken-Danish way to make a noun demonstrative.

• her = near the speaker
• der = farther away, or less immediate

Because pensel and rulle are common-gender nouns, Danish uses den. With a neuter noun, you would use det her or det der.

Both are possible, but they sound different in style.

• den her pensel = very common in everyday speech
• denne pensel = more formal, more written, sometimes a bit stiffer

So a learner will hear den her and den der a lot in normal conversation.

This is because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

The sentence starts with Med den her pensel, so that first phrase takes position 1. Then the finite verb must come next:

• Med den her pensel
  • kan
    • jeg
      • male

The same thing happens later:

• med den der rulle går det hurtigere

Here med den der rulle comes first, so går must come next.

Here med means with / by using. It tells you what tool is being used.

• Med den her pensel = with this brush
• med den der rulle = with that roller

It is repeated because each clause introduces a different tool. That is completely natural in Danish.

You could also say:

• ..., men det går hurtigere med den der rulle.

That version keeps the same meaning, but the original sentence puts extra emphasis on the contrast between the two tools.

No. male ved vinduet means paint by the window or paint near the window.

That is different from:

• male vinduet = paint the window itself

So the preposition ved is important.

• ved vinduet = at/by the window
• vinduet without ved could be the object being painted

Because vinduet is the definite form, meaning the window.

Danish usually adds definiteness to the end of the noun:

• et vindue = a window
• vinduet = the window

So ved vinduet means by the window.

If the meaning were less specific, you might say:

• ved et vindue = by a window

This is about grammatical gender.

• pensel is a common-gender noun
• rulle is a common-gender noun
• vindue is a neuter noun

Common-gender nouns use den in expressions like:

• den her pensel
• den der rulle

Neuter nouns use det in similar expressions:

• det her vindue
• det der vindue

And the definite singular form of vindue is vinduet.

Literally, it means something like goes it faster.

In natural English, that becomes:

• it goes faster
• it is faster
• it gets done faster

This is a very normal Danish way to talk about how quickly an activity happens.

In this sentence, the idea is that painting proceeds faster with the roller.

Here det is not referring to rulle.

If it referred to rulle, it would be strange, because rulle is common gender and would normally go with den, not det.

Instead, det is an impersonal subject, similar to English it in sentences like:

• It goes faster
• It is raining

So det går hurtigere means something like the process goes faster or it goes faster.

Hurtigere is the comparative form, meaning faster / more quickly.

Base forms:

• hurtig = fast
• hurtigt = fast / quickly
• hurtigere = faster / more quickly

In this sentence it works adverbially, describing how the action goes:

• går hurtigere = goes faster

So Danish does not need something like more quickly here; hurtigere does the job.

Sometimes it can, depending on tone of voice.

But in a sentence like this one, where it is clearly contrasting this brush with that roller, it is neutral and completely normal.

So:

• den her pensel ... den der rulle

just sets up a practical contrast between two objects.

If someone said den der with a certain annoyed tone, it could sound dismissive, a bit like English that ... thing.

Because of the structure around it.

In den der rulle, the word comes after a demonstrative phrase, so it must be a noun:

• den der rulle = that roller

If rulle were a verb, the structure would look different, for example:

• at rulle = to roll

So here rulle is clearly the name of a tool, not an action.

Yes, absolutely.

That version is also natural and means the same thing:

• Det går hurtigere med den der rulle.

The difference is emphasis.

• Med den der rulle går det hurtigere puts the tool first for contrast
• Det går hurtigere med den der rulle starts with the general statement and adds the tool afterward

Both are good Danish.