תרגום - טורקית-אנגלית - Selam. Evet, vaktim çok kısıtlı. ...

I don't have much time....> I have very limited time.
you can write to me...> There is no problem you can write to me

'yazmanda bir sakınca yok' is more like 'it's no problem for you to write to me'

and 'ama ben hemen cevap veremeyebilirim' is but I may not immediately be able to answer'.

- "vaktim çok kısıtlı" means "my time is very limited"

- I agree with Chantal for her second proposition but for "yazmanda bir sakınca yok", I think the translation given by Merdogan is the best. Because the person wants to say "you won't bother me if you write to me".