Buzlu kaldırımlarda yürürken zemin çok kaygandı.

Buzlu comes from buz (ice) + -lu (with, having, covered in).

So buzlu means icy or covered with ice.

This -lu/-lü/-lı/-li suffix is very common in Turkish:

• tuz → tuzlu = salty
• şeker → şekerli = sugary
• sis → sisli = foggy

Here, buzlu kaldırımlar means icy sidewalks.

Kaldırımlarda breaks down like this:

• kaldırım = sidewalk / pavement
• -lar = plural
• -da = locative suffix, meaning in / on / at

So kaldırımlarda means on the sidewalks.

A few useful notes:

• English uses on with sidewalks, but Turkish uses the locative -da/-de, which can cover in, on, at depending on context.
• The form is -lar rather than -ler because of vowel harmony.
• The form is -da rather than -ta because kaldırım ends in a voiced consonant.

Yes, it could be singular in another sentence, but here the plural sounds natural.

Kaldırımlarda can suggest:

• multiple sidewalk areas,
• sidewalks in general,
• or a general situation involving icy sidewalks.

Turkish sometimes uses the plural where English might prefer a more general singular expression. So this is not unusual.

Yürürken means while walking or when walking.

It is formed from:

• yürü- = to walk
• yürür = walks / is walking in a general or aorist-type form
• -ken = while / when

So:

yürürken = while walking

This -ken structure is very common:

• yemek yerken = while eating
• konuşurken = while speaking
• eve giderken = while going home

That is a very common question.

Yürürken itself does not show person clearly the way an English clause would. The subject is usually understood from context.

So in this sentence, the walker is not explicitly named. The sentence is basically giving a situation:

• while walking on the icy sidewalks...
• the ground was very slippery

This can feel slightly odd to an English speaker, because English usually wants the subject of while walking to be very clear. Turkish is often more comfortable leaving that to context.

Zemin means ground, surface, floor.

In this sentence, zemin refers to the surface underfoot — the part you are walking on.

Compared with yer:

• yer is more general: place, spot, ground
• zemin is more specific: surface, flooring, ground surface

So zemin çok kaygandı focuses on the walking surface being slippery.

Yes. Kaygandı means was slippery.

It comes from:

• kaygan = slippery
• -dı = past tense copula

So:

kaygan = slippery
kaygandı = was slippery

This is how Turkish often makes past statements with adjectives:

• hava soğuk = the weather is cold
• hava soğuktu = the weather was cold
• zemin kaygan = the ground is slippery
• zemin kaygandı = the ground was slippery

In the present tense, Turkish often has no separate word for is:

• zemin çok kaygan = the ground is very slippery

But in the past, the past marker appears:

• zemin çok kaygandı = the ground was very slippery

No. Here it comes from kaygan (slippery), not kaygı (worry, anxiety).

They may look similar at first, but they are different words:

• kaygan = slippery
• kaygı = anxiety, worry

So in this sentence, kaygandı definitely means was slippery.

Çok means very here.

So:

• kaygandı = was slippery
• çok kaygandı = was very slippery

This is straightforward adjective modification in Turkish:

• çok güzel = very beautiful
• çok soğuk = very cold
• çok kaygan = very slippery

Turkish does not need anything like an English -ly form here.

Because Turkish is usually predicate-final.

The sentence is arranged like this:

• Buzlu kaldırımlarda yürürken = background / setting
• zemin = subject
• çok kaygandı = predicate

So the overall order is very natural for Turkish. English often prefers to place the main verb earlier, but Turkish commonly keeps the main predicate at the end.