"I am a woman."
You probably mean the accusative suffix. You don't use it, when you refer to something in general.
Elma yerim. - I eat an apple or apples.
Elmayı yerim. - I eat the apple.
This doesn't apply to the "to be"-suffix which you almost always have to use. There are exceptions like "Bizim ev.", but that could be colloquial and shouldn't bother you.
Yes, this is the rule on the accusative case. This rule only applies to the accusative case, i.e. the accusative case marker is used only for definite objects.
There is a debate whether or not there are six or seven cases in Turkish.
The cases are:
And then, there is the word "ile" that some people consider as a case. You can use "ile" separately or as an ending, "Arabayla eve gidiyorum".