Після душу я витираю волосся рушником.

Because Після душу is just a short time phrase at the beginning of the sentence. In normal Ukrainian punctuation, that kind of introductory adverbial phrase usually does not need a comma.

So the neutral standard version is:

Після душу я витираю волосся рушником.

A comma would only appear if the writer wanted an unusual pause or a special stylistic effect.

Because після requires the genitive case.

So the noun душ changes form after після:

• душ = shower
• після душу = after a shower

This is a very common pattern in Ukrainian:

• після уроку = after the lesson
• після обіду = after lunch
• після роботи = after work

So the main thing to remember is:

після + genitive

In everyday Ukrainian, після душу very naturally means after taking a shower / after showering.

So even though the noun is literally shower, the whole phrase works like English after a shower.

If you want to be more explicit, you could say something like:

• після того, як я прийняв душ = after I took a shower (male speaker)
• після того, як я прийняла душ = after I took a shower (female speaker)

But після душу is shorter and very natural.

In Ukrainian, волосся is usually treated as a collective noun meaning hair as a whole. Grammatically, it is neuter singular, even though it refers to many individual hairs.

That is why you say things like:

• моє волосся = my hair
• довге волосся = long hair
• мокре волосся = wet hair

So in this sentence, волосся means the hair on my head, not individual hairs one by one.

It is the direct object of the verb, so logically it is in the accusative case.

But for many inanimate neuter nouns in Ukrainian, the accusative looks exactly the same as the nominative. So:

• nominative: волосся
• accusative: волосся

That is why you do not see a visible change here.

Рушником is the instrumental case of рушник.

Ukrainian often uses the instrumental to show the tool, means, or instrument used to do something.

So:

• рушник = towel
• рушником = with a towel / by means of a towel

This is very common:

• писати ручкою = to write with a pen
• їсти ложкою = to eat with a spoon
• відчинити ключем = to open with a key

So витираю волосся рушником literally means I wipe/dry my hair using a towel.

Not exactly.

Витираю comes from витирати, which means to wipe or to dry by wiping. In this sentence, it suggests towel-drying.

So:

• витираю волосся рушником = I towel-dry / wipe-dry my hair

By contrast, сушу from сушити is more general:

• Я сушу волосся феном. = I dry my hair with a hairdryer.

So витираю focuses on the action of wiping with the towel, while сушу just focuses on making something dry.

It can mean either, because витираю is an imperfective present-tense form.

Depending on context, it can mean:

• I am drying/wiping my hair now
• I dry/wipe my hair regularly, as part of a routine

In this sentence, with після душу, many people will understand it as a habitual routine:

After a shower, I towel-dry my hair.

If you wanted a clearly completed future action, you would normally use a perfective form, for example:

Після душу я витру волосся рушником.
= After the shower, I’ll dry my hair with a towel.

No, and no.

1. Я can be omitted

Ukrainian often leaves out subject pronouns because the verb ending already shows the person.

So both are possible:

• Після душу я витираю волосся рушником.
• Після душу витираю волосся рушником.

Including я can add a little emphasis or clarity.

2. Word order is flexible

The given order is neutral and natural. It starts with the time phrase, then the subject, then the action.

Other orders are also possible, but they change the emphasis a bit:

• Я після душу витираю волосся рушником.
  Slightly more emphasis on I.

• Я витираю волосся рушником після душу.
  The time phrase comes later, so it gets a different rhythm/focus.

So the original sentence is a very normal, natural way to say it, but it is not the only possible word order.