Ben akşam yürüyüşünden sonra bir mandalina soyup çayın yanında yiyorum.

That’s right: Turkish often omits subject pronouns because the verb already shows the person.

• yiyorum already means I am eating / I eat
• So Ben is not strictly necessary

You can say:

• Akşam yürüyüşünden sonra bir mandalina soyup çayın yanında yiyorum.

Adding Ben can give:

• extra emphasis
• contrast, as in I do this, not someone else
• a slightly more explicit style

So Ben is optional here.

It breaks down like this:

• akşam = evening
• yürüyüşü = walk, in the compound akşam yürüyüşü
• -nden / -den = from
• sonra = after

Together, akşam yürüyüşünden sonra means after the evening walk or after my evening walk, depending on context.

A key point is that Turkish often uses a noun compound where English just uses two nouns:

• akşam yürüyüşü = evening walk

So this is a very normal Turkish structure.

Because the full base expression is akşam yürüyüşü.

In Turkish, akşam yürüyüşü is a noun compound, and the second noun takes a suffix that looks like a possessive ending:

• akşam yürüyüşü = evening walk

When you add a case ending to a noun that already has that suffix, Turkish usually inserts a buffer n:

• yürüyüşü + den → yürüyüşünden

So:

• akşam yürüyüşünden sonra = after the evening walk

This is a very common pattern in Turkish noun compounds.

Here bir works like a/an in English.

So:

• bir mandalina = a tangerine / a mandarin

It can also literally mean one tangerine, but in this sentence it most naturally just introduces an indefinite object: a tangerine.

Because Turkish usually leaves an indefinite direct object unmarked.

So:

• bir mandalina yiyorum = I am eating a tangerine
• mandalinayı yiyorum = I am eating the / that specific tangerine

In your sentence, bir mandalina is indefinite, so no accusative is needed.

Very roughly:

• unmarked object = non-specific or newly introduced
• accusative-marked object = specific, definite, or already identifiable

soyup comes from soymak, which means to peel.

The ending -ip / -ıp / -up / -üp is a very common converb ending in Turkish. It links actions done by the same subject.

So:

• soyup yiyorum = I peel it and eat it / I peel it, then eat it

It is a compact way to connect verbs without repeating the subject.

The form is soyup because of vowel harmony.

This pattern is extremely common:

• alıp geldim = I bought it and brought it
• oturup bekledim = I sat down and waited
• soyup yiyorum = I peel it and eat it

Usually it suggests a sequence:

• first I peel it
• then I eat it

The -ip form can sometimes just mean and, but in a sentence like this the natural interpretation is peel and then eat.

So the English idea is:

• I peel a tangerine and eat it with tea
• or After my evening walk, I peel a tangerine and then eat it with tea

Because Turkish often leaves repeated information unstated if it is already clear.

So:

• bir mandalina soyup yiyorum

naturally means:

• I peel a tangerine and eat it

Even though there is no separate word for it, the object is understood from bir mandalina.

English often repeats the object or uses it, but Turkish does not need to.

çayın yanında is a very common way to say with tea in the sense of alongside tea or served with tea.

It literally breaks down as:

• çay-ın = of the tea
• yan-ı-nda = at its side / by its side

So literally it is something like:

• at the side of the tea

But idiomatically, in food-and-drink contexts, it means:

• with tea
• alongside tea

çayla is also possible in some contexts, but çayın yanında sounds very natural when talking about something eaten as an accompaniment to tea.

It can be both.

Literal meaning:

• physically next to the tea

Idiomatic meaning in food contexts:

• eaten or served with tea

In this sentence, the idiomatic food meaning is the most likely one:

• I eat it with tea

Both are possible, but they give slightly different nuances.

• yiyorum = I am eating / I eat
• yerim = I eat, more generally or habitually

In everyday Turkish, -iyor forms are often used not only for something happening right now, but also for a personal routine or something one commonly does.

So this sentence can sound like:

• something I’m doing now
• or a casual description of my usual habit

If you said:

• Ben akşam yürüyüşünden sonra bir mandalina soyup çayın yanında yerim

that would sound more plainly habitual: I eat a tangerine with tea after my evening walk.

Not completely. Turkish word order is flexible, although the verb usually stays near the end.

Your sentence is natural as it is:

• Ben akşam yürüyüşünden sonra bir mandalina soyup çayın yanında yiyorum.

But other orders are also possible, depending on emphasis:

• Akşam yürüyüşünden sonra bir mandalina soyup çayın yanında yiyorum.
• Ben bir mandalina akşam yürüyüşünden sonra soyup çayın yanında yiyorum.
• Akşam yürüyüşünden sonra çayın yanında bir mandalina soyup yiyorum.

The meaning stays similar, but the focus shifts a little.

A useful basic idea is:

• time expressions often come early
• the main verb often comes last
• elements before the verb can be moved around for emphasis

Usually, no.

In a simple Turkish sentence like this, a comma is normally unnecessary:

• Ben akşam yürüyüşünden sonra bir mandalina soyup çayın yanında yiyorum.

In English, a comma after an opening time phrase is often optional or stylistic:

• After my evening walk, I peel a tangerine and eat it with tea.

But Turkish punctuation is generally lighter in this kind of structure.