Does - As you cogitate make sense in a sentence?

No. Cogitate is both transitive and intransitive, that is we may cogitate something and cogitate about something. But we do not cogitate that... in the sense of forming an opinion about it.

No, you would say "She said".But you can say, "said her friend".

No, it should say "It does not make any sense," or "It makes no sense."

No

I don't know the make and model of the camera, but I saw at the trade fair.I'm going to make a gingerbread cake for the bake sale.You know, if you don't pick up your room, your mother will make you...