Learn Hardcore Polish: Tabletki i syrop stoją na stole w kuchni. - The pills and the syrup are on the table in the kitchen.

The basic dictionary form is tabletka (singular: a pill, a tablet).
Tabletki is nominative plural, used here as the subject of the sentence.
So the subject is tabletki i syrop = pills and syrup.

What gender are tabletka and syrop, and does that affect the sentence?

Tabletka is feminine.
Tabletki is therefore a feminine plural form.
Syrop is masculine inanimate (like stół, dom, etc.).

Together, tabletki i syrop form a plural subject. That is why the verb is plural (stoją).
Gender does not change the verb form in the present tense, but it would matter in the past tense and with adjectives (e.g. Tabletki i syrop były / stały).

Why is the verb stoją plural and not singular, when syrop is singular?

Because the whole subject is plural:

Subject: tabletki i syrop = pills and syrup → more than one thing.
With a compound subject joined by i (and), Polish always uses a plural verb.

So:

Tabletki i syrop stoją… = correct
Tabletki i syrop stoi… = ungrammatical in standard Polish

What does stoją literally mean, and why not just use są?

Stoją is the 3rd person plural of stać = to stand.
Literally: Tabletki i syrop stoją… = The pills and syrup are standing…

In Polish, verbs like stać (stand), leżeć (lie), siedzieć (sit) are very often used instead of plain być (są, to be) to describe objects and their position:

stoją – they are upright / standing (bottles, boxes, jars, etc.)
leżą – they are lying (flat things, things lying on their side)

You could say Tabletki i syrop są na stole w kuchni, and it is correct, but stoją sounds more natural if you imagine (for example) a bottle of syrup and a box of pills standing upright.

When would you say leżą instead of stoją for things on a table?

Use:

leżą (from leżeć) if the items are lying flat or on their side:
- Tabletki i syrop leżą na stole – e.g. loose pills and a bottle knocked on its side.
stoją (from stać) if the items are upright:
- Tabletki i syrop stoją na stole – e.g. a box of pills and a bottle standing.

Native speakers are quite sensitive to this difference in everyday descriptions.

What case is na stole, and why is it not na stół?

Na stole is locative singular of stół (table).

The preposition na can take two cases:

Locative for location (where?):
- na stole – on the table (no movement, just location)
Accusative for direction / movement (onto where?):
- na stół – onto the table (movement toward the table’s surface)

In this sentence we are describing where the objects are, not where they are being put, so we use na stole (locative), not na stół.

What case is w kuchni, and what is the rule for w?

W kuchni is also locative singular (of kuchnia – kitchen).

Preposition w works similarly to English in:

w
- locative = location (where?):
  - w kuchni – in the kitchen
w
- accusative = direction / into (where to?):
  - Dochodzę w kuchnię is not natural; instead Polish prefers idę do kuchni (I’m going to the kitchen).
    So with movement towards, we typically use do
    - genitive, not w.

For our sentence we need simple location in the kitchen, so w kuchni is locative.

How do stół → stole and kuchnia → kuchni change grammatically?

Both are examples of the locative singular:

stół (table, masculine)
- Nominative: stół – the table (subject)
- Locative: stole – after na in a static location: na stole
kuchnia (kitchen, feminine)
- Nominative: kuchnia – the kitchen (subject)
- Locative: kuchni – after w: w kuchni

So in na stole w kuchni, both stole and kuchni are locative forms triggered by na and w describing where something is.

Can you change the word order in this sentence?

Yes. Polish word order is quite flexible. All of these are grammatically correct:

Tabletki i syrop stoją na stole w kuchni.
Na stole w kuchni stoją tabletki i syrop.
W kuchni na stole stoją tabletki i syrop.
W kuchni stoją na stole tabletki i syrop.

The basic meaning stays the same. Changes mainly affect:

What is emphasized (for example, starting with w kuchni highlights the kitchen as the setting).
The rhythm and style of the sentence.

The version you gave is a very natural, neutral word order.

Why is there no word for the or some before tabletki and syrop?

Polish has no articles like English a / an / the.

tabletki can mean pills, the pills, or some pills.
syrop can mean syrup, the syrup, or some syrup.

Definiteness or indefiniteness is understood from:

The context (are we talking about specific pills we already know?).
Word order and stress.
Additional words like te tabletki (these pills), jakiś syrop (some syrup).

So Tabletki i syrop stoją na stole w kuchni could be translated as:

The pills and (the) syrup are on the table in the kitchen
or
Some pills and some syrup are on the table in the kitchen, depending on context.

Is there any difference between tabletki i syrop stoją and syrop i tabletki stoją?

Grammatically, they are the same: both give you a plural subject and require stoją.

The difference is only in information order:

The first-mentioned item tends to sound a bit more important or more expected in that context.
If you say Tabletki i syrop…, it suggests pills are a bit more in focus.
If you say Syrop i tabletki…, the syrup feels slightly more prominent.

In everyday speech, people often list things in whatever order feels natural to them; both orders are common.

How do you pronounce stoją and kuchni?

Approximate pronunciation:

stoją: [STOY-on], with a nasal ą at the end:
- sto like stoy in stoyan,
- -ją / -ą is nasal; many learners say it like -on, which is close enough.
kuchni: [KOOH-kh-nee]
- ch is like German ch in Bach, a voiceless kh sound.
- ni here is pronounced with a soft ń sound, similar to Spanish ñ in niño.

More precisely in IPA:

stoją: [ˈstɔjɔ̃] (often heard as [ˈstɔjɔm] in casual speech)
kuchni: [ˈkuxɲi]

Can you omit w kuchni or na stole?

Yes, but you lose information:

Tabletki i syrop stoją na stole.
– The pills and syrup are on the table. (We don’t know where the table is.)
Tabletki i syrop stoją w kuchni.
– The pills and syrup are in the kitchen. (We don’t know exactly where in the kitchen.)
Tabletki i syrop stoją.
– The pills and syrup are standing. (Very incomplete; the listener will expect you to say where.)

The full sentence Tabletki i syrop stoją na stole w kuchni tells us precisely: standing on the table, which is in the kitchen.

Does syrop mean specifically medicine here, or could it be food syrup?

The word syrop by itself just means syrup. It can be:

medical syrup: syrop na kaszel – cough syrup,
food syrup: syrop malinowy – raspberry syrup, syrop klonowy – maple syrup.

In your sentence, because it appears together with tabletki (pills), most listeners will naturally assume it’s medical syrup (e.g. cough syrup), but grammatically it could be any kind of syrup.

How would this sentence look in the past tense?

You would mainly change the verb:

Present: Tabletki i syrop stoją na stole w kuchni.
– The pills and syrup are (standing) on the table in the kitchen.
Past: Tabletki i syrop stały na stole w kuchni.
– The pills and syrup were (standing) on the table in the kitchen.

Notes:

stały is 3rd person plural past, non‑masculine‑personal, which we use for mixed inanimate things like tabletki (feminine) and syrop (masculine inanimate).
The nouns and prepositional phrases (na stole, w kuchni) stay the same.