Geç kalmamın sebebi trafikti.

The full phrase geç kalmamın means roughly of my being late.

A simple breakdown is:

• kalmak = to stay / remain
• geç kalmak = to be late
• kalma = being late (a verbal noun)
• kalmam = my being late
• kalmamın = of my being late

So in this sentence, Turkish turns to be late into a noun-like idea: my being late.

No. Here, -ma is a verbal noun / nominalizing suffix, not negation.

That is a very common confusion, because Turkish also uses -ma/-me for negation.

In this sentence:

• kalma = being late

If you really wanted the negative, you would get something like:

• kalmamamın = of my not being late

So:

• kalmamın = of my being late
• kalmamamın = of my not being late

That -ın is the genitive ending.

Turkish often uses a structure like:

• X-in sebebi = the reason for/of X

So here:

• geç kalmamın = of my being late
• sebebi = its reason / the reason

Together:

• geç kalmamın sebebi = the reason for my being late

This is a standard Turkish genitive + possessed noun pattern.

Because the phrase uses a possessive construction.

In Turkish, when you say something like the reason for X, the noun reason takes a possessive ending:

• sebep = reason
• sebebi = its reason / the reason for it

So:

• kalmamın sebebi = the reason for my being late

Also, note the sound change:

• sebep + i becomes sebebi

The final p often changes to b before a vowel in Turkish.

So it is sebebi, not sebepi.

Trafikti means it was traffic or simply was traffic.

It comes from:

• trafik = traffic
• idi = was

So:

• trafik idi → trafikti

The d changes to t because it follows the voiceless consonant k. This is a normal sound change in Turkish.

So the sentence ends with a past-tense noun predicate:

• trafikti = was traffic

Because Turkish often puts that information into suffixes instead of using a separate pronoun.

In kalmamın:

• -m shows first person singular: my
• -ın is the genitive ending

So my is already built into the word.

You can say:

• Benim geç kalmamın sebebi trafikti.

But that adds emphasis or contrast, something like the reason for my being late...

Most of the time, benim is unnecessary here.

Because geç kalmak is a fixed expression meaning to be late.

• geç = late
• kalmak = the verb part

The endings attach to kalmak, not to geç:

• geç kaldım = I was late
• geç kalmak = to be late
• geç kalmamın = of my being late

So geç stays the same, and kal- carries the grammar.

Because this sentence is not built as because of traffic.

It is built as:

• The reason for my being late was traffic.

So trafik is just the noun predicate at the end, and it does not need an extra case ending.

If you wanted a more direct because of traffic structure, Turkish could use:

• Trafik yüzünden geç kaldım.
• Trafikten dolayı geç kaldım.

Those are different sentence patterns.

This sentence is natural, but it sounds a bit more explanatory or formal than everyday casual speech.

A very common conversational alternative is:

• Geç kaldım çünkü trafik vardı.
  = I was late because there was traffic.

Your original sentence is more like calmly stating the cause:

• Geç kalmamın sebebi trafikti.

So both are correct, but they have slightly different style and tone.

Yes, but the usual Turkish order here is very natural:

• Geç kalmamın sebebi trafikti.

Turkish often puts the main predicate at the end.

You can also say:

• Trafik geç kalmamın sebebiydi.

That means essentially the same thing, but the emphasis shifts a bit more toward traffic.

Notice that in this version:

• sebebiydi = sebebi + idi = was the reason

So the sentence can be rearranged, but the original order is a very standard one.