Could smoking an occcasional cigarette potentially cause damage to a voice if I want to be a serious singer? I'm talking only 6 a week, one day or every second day?

Yes. Smoking dries out the inside of your mouth, and wreaks havoc on the vocal chords.

Would it take immediate effect? Or appear over time? How long if over time?

Why would you even want to risk it? You do know that nicotine is addictive right? 6 a week now could be a pack a day next month.

Not to mention, OP's 16...

... you're not even old enough to smoke.

The nicotine doesn't have an addictive effect on me and I can go weeks without one, I just like the occasional one every now and then.

Not to mention, OP's 16...

...you're not even old enough to smoke.

True, in the US it is illegal at this age.

I'm not in the us, its legal where I am.

So, it's still a drug, and it's still addictive. Why would you want to start such a horrible addiction if you want to save your vocal cords for singing?