can anyone tell me what the rules or regarding using the word/letter "o"
as in: o zaman .....

There are no specific rules pertaining to the use of 'o', the third person singular pronoun. So, i will just give a few examples in the hope that they may help.

- Mac iptal olmus. / The game has been cancelled.
- O zaman sinemaya gidelim. / 'IN THAT CASE' let's go to the movies.

'o zaman' refers to a contextual situation that is clear to the speakers. Zaman does not refer to a 'time frame' as the definiton of 'zaman' would suggest. It is identical to 'o halde' meaning 'in that case or under the circumstances'.

- O zaman bizde eve gideriz. / In that case, we will just go home.

- Iyi o zaman! Gorursun sen gununu. / ok, in that case, you'll see what will happen to you.

- O zaman bende seni polise sikayet ederim. / If that's tha case, then, I will report you to the police.

- O zamanlarda Turkler Orta Asyadalarmis. / In those days, Turks were living in Central Asia. (Mark the fact that o zamanlar in this case is actually referring to a time frame, but only if it is used in the plural form).

- O kadar cok istedi ki hayir diyemedim. / He asked for it so much that I couldn't say no.
- o kadar cok israr etti ki sonunda evet dedim. / He insisted so much that, eventually, I said yes.

Actually, I just read my post, and it sounds a bit weak. I hope someone else will be able provide a better clarification. In the mean time, I will think of a better answer to your inquiry.

One thing you can be assured of is that the use of 'o' is based on context. Usually, the context is clear to the speakers referring to something that both parties are aware of. I hope this helps a bit.