Masz może jakąś chusteczkę? Od rana kicham i trochę kaszlę.

Both are possible.

• Masz może jakąś chusteczkę? = very natural in everyday speech
• Czy masz może jakąś chusteczkę? = also correct, a bit more explicit as a yes/no question

In Polish, you can often make a yes/no question with just intonation, without adding a separate word like English do.

So Masz...? is simply Do you have...?

Here może does not literally mean maybe in the full English sense. It is a softening particle.

Masz może jakąś chusteczkę? means something like:

• Do you maybe have a tissue?
• Do you happen to have a tissue?
• Would you by any chance have a tissue?

It makes the request sound less direct and more polite/casual.

Because after masz the thing you have is the direct object, so it goes in the accusative case.

Base forms:

• jakaś = some / a certain
• chusteczka = tissue / handkerchief

Accusative feminine singular forms:

• jakąś
• chusteczkę

So:

• jakaś chusteczka = nominative, dictionary/basic form
• jakąś chusteczkę = accusative, used after masz

Yes, roughly. In this sentence jakąś means something like:

• some
• any
• a

So Masz jakąś chusteczkę? is like:

• Do you have a tissue?
• Do you have any tissue / any tissue on you?

In Polish, adding jakąś makes the request sound a bit more natural and less abrupt than just Masz chusteczkę?

It can mean tissue or small handkerchief, depending on context.

In this sentence, because the speaker is sneezing and coughing, chusteczka will normally be understood as a tissue.

If you want to be very specific, Polish also has:

• chusteczka higieniczna = paper tissue

But in normal conversation, chusteczka is often enough.

Polish usually omits subject pronouns when they are clear from the verb form.

• Masz already means you have
• kicham already means I sneeze / I’m sneezing
• kaszlę already means I cough / I’m coughing

So adding ty or ja is usually unnecessary unless you want emphasis or contrast.

Literally, od rana is from morning or from the morning, but idiomatically it means:

• since morning
• since this morning
• all morning (depending on context)

Grammar:

• od takes the genitive
• the genitive of rano / ranek here is rana

So od rana is a fixed, very common expression.

Because in Polish, the present tense is used for actions or states that:

• started earlier
• are still continuing now

So Od rana kicham i trochę kaszlę is a natural way to say:

• I’ve been sneezing and coughing a bit since this morning

English often uses the present perfect continuous, but Polish normally just uses the present tense here.

Trochę means:

• a little
• a bit
• somewhat

So:

• kaszlę = I’m coughing
• trochę kaszlę = I’m coughing a bit

It softens the statement and makes it more specific. It is very natural when talking about symptoms.

It is a normal present-tense form, but it can look odd to learners.

Infinitive:

• kaszleć = to cough

1st person singular:

• kaszlę = I cough / I’m coughing

Similarly:

• kichać = to sneeze
• kicham = I sneeze / I’m sneezing

So the sentence uses:

• kicham from kichać
• kaszlę from kaszleć

Those would change the meaning.

• Masz może jakąś chusteczkę? = Do you have a tissue?
• Mam chusteczkę? = Do I have a tissue? or, as a statement, I have a tissue
• Potrzebuję chusteczki = I need a tissue

So if you are asking another person for one, Masz może jakąś chusteczkę? is the right structure.

It is already natural and polite enough for everyday speech.

Levels:

• Masz chusteczkę? = direct, still normal
• Masz może chusteczkę? = softer, more polite
• Masz może jakąś chusteczkę? = very natural, slightly softer still

If you want to sound even more polite, especially to a stranger, you could say:

• Ma pan / ma pani może jakąś chusteczkę?

That is the formal you version.