Benim kırmızı ceketim kapının yanında asılı.

Yes, they both mark possession.

• benim = my / mine (the independent possessive pronoun, in genitive form)
• ceket-im = my jacket (the noun with a 1st person possessive suffix)

In Turkish, it is very common to mark possession on the noun itself:

• ceketim = my jacket

Adding benim makes it more explicit or emphatic:

• Benim ceketim = my jacket / my own jacket

So in many situations, Benim kırmızı ceketim... could also be simply:

• Kırmızı ceketim kapının yanında asılı.

The version with benim sounds a bit more specific, contrastive, or emphasized.

Because in Turkish, possession is normally shown with a possessive suffix on the noun.

So:

• ceket = jacket
• ceketim = my jacket

Using only benim ceket would sound incomplete or ungrammatical in standard Turkish. The normal pattern is:

• benim ceketim = my jacket
• senin ceketin = your jacket
• onun ceketi = his/her/its jacket

So the possessive suffix is not optional in this structure.

The adjective stays before the noun, and the possessive suffix attaches to the noun, not to the adjective.

Structure:

• kırmızı = red
• ceket-im = my jacket
• kırmızı ceket-im = my red jacket

So Turkish keeps this order:

possessor + adjective + noun + possessive suffix

Example from the sentence:

• Benim kırmızı ceketim

Not:

• benim kırmızım ceket
• benim ceket kırmızı-im

The suffix belongs to the noun ceket.

This is because Turkish often uses a construction that literally works like:

• kapı-nın yan-ı = the door’s side
• kapı-nın yan-ı-nda = at the side of the door / next to the door

Breakdown:

• kapı = door
• kapı-nın = of the door
• yan = side
• yan-ı = its side / the side
• yanında = at its side / beside it

So kapının yanında means next to the door or by the door.

This is a very common Turkish pattern:

• evin önünde = in front of the house
• masanın üstünde = on the table
• okulun yanında = next to the school

Yanında is built from the noun yan (side) plus suffixes.

Breakdown:

• yan = side
• yan-ı = its side / the side
• yan-ın-da = at its side

In the full phrase:

• kapının yanında = at the door’s side = next to the door

So Turkish often uses body-part or location nouns like yan (side), üst (top), alt (bottom), ön (front), arka (back) in these kinds of expressions.

Asılı is usually understood here as an adjectival/predicate form meaning hanging or hung up.

So the sentence is describing the state of the jacket:

• The jacket is hanging by the door.

It is not functioning like an ordinary conjugated verb such as asıyor or asıyor would. Instead, it behaves more like a descriptive predicate.

You can think of it roughly like:

• asılı = in a hung position / hanging

So the whole sentence is essentially:

• My red jacket is hanging next to the door.

Because Turkish often leaves out the verb to be in the present tense when the predicate is a noun, adjective, or similar descriptive form.

So:

• Ceket asılı. = The jacket is hanging.
• Kapı açık. = The door is open.
• O mutlu. = He/She is happy.

In the 3rd person present, there is usually no separate word for is/are.

So:

• Benim kırmızı ceketim kapının yanında asılı. naturally means
• My red jacket is hanging next to the door.

Yes, absolutely.

A very natural version is:

• Kırmızı ceketim kapının yanında asılı.

Since ceketim already means my jacket, benim is not necessary unless you want emphasis, contrast, or extra clarity.

For example:

• Benim kırmızı ceketim kapının yanında asılı, seninki dolapta. = My red jacket is hanging by the door, yours is in the closet.

Here benim helps create contrast with seninki.

The sentence is natural as written, but Turkish word order is somewhat flexible.

The neutral order here is:

• Benim kırmızı ceketim
  • kapının yanında
    • asılı

This is basically:

• subject
  • location
    • predicate

You could also hear:

• Kırmızı ceketim kapının yanında asılı.
• Kapının yanında benim kırmızı ceketim asılı.

Changing the order can shift emphasis:

• starting with kapının yanında highlights the location
• starting with benim kırmızı ceketim highlights the jacket

But the original sentence is completely natural.

Because Turkish possessive suffixes follow vowel harmony and sound rules.

The 1st person singular possessive suffix is basically:

• -ım / -im / -um / -üm

Which version appears depends on the last vowel of the noun.

In ceket, the last vowel is e, so the correct form is:

• ceket-im

More examples:

• kitap → kitabım = my book
• ev → evim = my house
• okul → okulum = my school
• gül → gülüm = my rose

So ceketim follows normal Turkish vowel harmony.

That ending is the genitive suffix, used for of relationships.

The genitive has several forms depending on vowel harmony:

• -ın / -in / -un / -ün

After kapı, the correct form is:

• kapı-nın

So:

• kapının yanında = at the side of the door

This is not random; it follows regular Turkish patterns.

Compare:

• evin önü = the front of the house
• masanın üstü = the top of the table
• arabanın arkası = the back of the car

In standard Turkish for this meaning, kapının yanında is the normal form.

That is because yanında belongs to a construction that usually requires the thing before it to be in the genitive:

• kapının yanında
• evin önünde
• masanın üstünde

So kapı yanında would generally sound wrong or incomplete in standard usage for next to the door.

Not exactly.

• asılı usually describes a state: hanging / hung up
• asılmış is a participle form that often feels more verbal, like hung or has been hung, depending on context

In this sentence, asılı is the most natural choice if you simply want to describe where the jacket is and what state it is in.

So:

• Ceket kapının yanında asılı. = The jacket is hanging by the door.

Using asılmış could sound more like you are focusing on the action/result of hanging it up, rather than just its current state.

Yes.

The sentence can be divided like this:

• Benim kırmızı ceketim = the thing being talked about
• kapının yanında = where it is
• asılı = its state

So the subject is:

• Benim kırmızı ceketim

And the rest tells you:

• location: kapının yanında
• condition/state: asılı