Bence

yazacaktım = I would have written

yazabilirdim = I could have written

yazardım = I would write

yazabilirim = I can write, I am able to write

-acak + dı  is also used as " about to do someting"

I was just about to phone you ---> Ben de tam sana telefon edecektim.

and also

FUTURE IN THE PAST

1. Structure: Yapı

Olumsuz şekli

Soru şekli

Henry,

I have learned in the class that we should have "swum" (pp of swim).

Marion either didn´t correct it. How come? Is that OK?

You are correct. My mistake. 

Swam is the past tense verb of swim, and swum is a past participle that needs to be used with an auxillery verb like have or had.

Unfortunately many English speakers like myself, do not know all our grammar rules. By learning Turkish, my English grammar knowledge has also slowly improved.

He swam in the Black Sea yesterday.

He had swum in the Black Sea before.

I have never swum in the Black Sea, but I swam in the Mediterranean Sea last year. 

Because we hardly ever use ´swum´, it sounds unusual and even wrong to many English speakers.