Yağmur yağınca kirpiklerim birbirine yapışıyor.

Yes, literally it looks that way.

• yağmur = rain (noun)
• yağmak = to rain / to fall (verb used for rain, snow, etc.)

So yağmur yağıyor is the normal Turkish way to say it is raining. Turkish does not use a dummy subject like English it in it is raining.

So yağmur yağınca is a very normal structure, not strange or redundant to a Turkish speaker.

-ınca / -ince / -unca / -ünce is a verb ending that usually means:

• when
• once
• whenever
• sometimes as soon as

So:

• yağınca = when it rains
• gelince = when he/she comes
• bitince = when it finishes

In this sentence, yağmur yağınca means when it rains.

It breaks down like this:

• kirpik = eyelash
• -ler = plural
• -im = my

So kirpiklerim literally means my eyelashes.

Turkish often attaches possession directly to the noun instead of using a separate word like English my.

Because that is the normal Turkish way to show possession.

Instead of saying a separate word every time, Turkish usually adds a possessive ending to the noun:

• elim = my hand
• saçım = my hair
• gözlerim = my eyes
• kirpiklerim = my eyelashes

You can add benim too, but that is usually for emphasis:

• benim kirpiklerim

In most situations, kirpiklerim by itself is enough.

birbiri means each other / one another.

Here it appears as birbirine, which includes the dative ending:

• birbiri = each other
• birbirine = to each other

So kirpiklerim birbirine yapışıyor means literally something like:

my eyelashes are sticking to each other

That is why the English meaning often becomes my eyelashes stick together.

Because the verb yapışmak normally goes with the dative ending -e / -a, meaning to stick to something.

Examples:

• duvara yapışmak = to stick to the wall
• elime yapıştı = it stuck to my hand
• birbirine yapışmak = to stick to each other

So birbirine is there because yapışmak wants a to-type complement.

This is a very common question.

In Turkish, plural subjects do not always require a plural verb the way they do in English. With non-human plural subjects, singular verb forms are especially common and natural.

So:

• kirpiklerim birbirine yapışıyor = natural
• kirpiklerim birbirine yapışıyorlar = not natural here

Since eyelashes are non-human, the singular verb form yapışıyor is the normal choice.

Yes, and Turkish -yor can do that.

Although -yor is often taught as is doing, it is also used for:

• things happening now
• repeated situations
• typical behavior in a certain context
• personal observations

So here yapışıyor can mean something like:

• my eyelashes are sticking together
• my eyelashes stick together

depending on context.

A more general or timeless version could also use yapışır, but yapışıyor sounds very natural in everyday speech.

The Turkish ğ is usually not pronounced like a hard English g.

In many words, it:

• lengthens the vowel before it, or
• creates a very soft transition

So:

• yağmur sounds roughly like yaa-mur
• yağınca sounds roughly like yaa-ınca

The important thing is: do not pronounce it like the g in go.

Turkish word order is flexible, but this version is very natural.

Putting Yağmur yağınca first sets up the situation first:

• When it rains, ...

That is a common and smooth way to structure the sentence.

You could move things around, but the original order is the most neutral and natural for everyday use.