Architektka pokazuje nam plan nowego domu.

Architektka is the feminine form of architekt (architect).

• architekt = a male architect
• architektka = a female architect

Since the sentence is talking about a woman, Polish uses architektka. Polish often marks professions for gender, especially when referring to a specific person.

Pokazuje is the 3rd person singular present tense of the verb pokazywać (to show).

So it means:

• (on/ona/ono) pokazuje = he/she/it shows

Here it matches architektka, which is singular, so pokazuje means she shows.

Because nam means to us, while my means we.

The verb pokazywać often works like to show someone something:

• pokazać/pokazywać komuś coś
• literally: to show to someone something

So in this sentence:

• nam = to us / us

It is the dative case form of my.

A quick comparison:

• my = we
• nas = us
• nam = to us

Here the architect is showing us the plan, so nam is the correct form.

Because the two nouns play different roles in the sentence.

• plan is the direct object of pokazuje, so it stays in the accusative
• For an inanimate masculine noun like plan, the accusative singular looks the same as the nominative singular: plan

But domu is part of the phrase nowego domu = of the new house, and after a noun like plan, Polish often uses the genitive to express of something.

So:

• plan = plan
• domu = of the house

That is why dom changes to domu.

Because after plan, Polish uses a structure equivalent to plan of the new house.

That means house must be in the genitive singular:

• dom → domu

And the adjective must match it in case, gender, and number:

• nowy → nowego

So:

• nowy dom = a new house (basic form)
• nowego domu = of a new house / of the new house

In this sentence, Polish needs the second one.

Polish has no articles, so there is no direct equivalent of a or the.

So plan nowego domu can mean:

• a plan of a new house
• the plan of a new house
• sometimes even the plan of the new house

The exact meaning depends on context. Polish usually leaves that unstated unless something else makes it clear.

Yes, Polish word order is fairly flexible.

The neutral order here is:

• Architektka pokazuje nam plan nowego domu.

This sounds natural and straightforward: The architect is showing us the plan of the new house.

But other orders are possible for emphasis, for example:

• Architektka nam pokazuje plan nowego domu.
• Plan nowego domu architektka pokazuje nam.

These are grammatically possible, but they shift emphasis or sound more marked. For learners, the original order is the safest and most natural.

It can mean both, depending on context.

Polish present tense often covers both:

• she shows
• she is showing

So Architektka pokazuje nam plan nowego domu could mean:

• The architect shows us the plan of the new house
• The architect is showing us the plan of the new house

English makes a stronger distinction here than Polish does.

Pokazywać is the imperfective verb.

It is used for:

• ongoing actions
• repeated actions
• general present-tense statements

Its perfective partner is usually pokazać.

So:

• pokazywać = to be showing / to show (imperfective)
• pokazać = to show, to reveal, to show once/completely (perfective)

In the present tense:

• pokazuje from pokazywać = she shows / is showing

The perfective verb pokazać does not normally describe a present ongoing action; its present-tense forms usually refer to the future:

• pokaże = she will show

A rough English-friendly pronunciation is:

• ar-khee-TEKT-ka

A few details:

• ch in Polish is like a hard h sound
• i before e helps soften the sound a little
• ktk is a real consonant cluster, so the middle is compact: tek-tka
• stress in Polish is usually on the second-to-last syllable, so here it falls on tekt

So the stress is: archiTEKTka

Because Polish has no articles.

English says:

• the plan
• a house

Polish simply says:

• plan
• dom

Whether something is a or the is understood from context. That is normal in Polish and one of the big differences from English.