In my earlier days of cat rescue and adoption, I was rather unfamiliar with cats as an ethnic group and carefully studied the sounds they made. The cats were all from the street and raised by different mamas, which apparently had some bearing on the diversity of their talking except for certain plaintive cries for mama or food, or to express acute distress and fear. No two or three cats seemed to have the same vocabulary.
I have had my large inter-species family now for over 5 years, and I find that the longer a cat stays with me, the more accurately they adopt the vocabulary of each other, until I can often tell a newcat from the old group just by the way they ask for things or greet me. Even in the dark of night, I can usually say -- that is one of the family, not a newcat.
I also found that the longer the cats related to me and to each other, the more chatty they became. Originally I had a siamese mix, who talked all the time, while the others mostly confined themselves to demanding something or saying hello. Perhaps because the siamese taught the others, or perhaps because I carry on continuous and lengthy discussions with each cat, they all developed the accepted Cat's Pride language. Some of them have also adopted a yip-yip like the dogs when they want my attention. As to body language, the cats relate to each other much in stereotypical fashions, but they alter their behaior to various degrees with the dogs -- less tail waving, more coolness and less sudden movement or growling, which they have learned freaks the dogs out. They also almost don't talk to the dogs unless they have had a frightening experience and are broadcasting generally their story. The dogs also do that. Both dogs and cats respond to such cries and exhibit sympathy by licking, rubbing, or literally clutching each other.
But a note on the chattering sound cats make with their teeth. They are not looking AT something, Debra. They are preparing to attack it. The teeth clicking is a sign of the hunter as he/she spots a bird or squirrel, or even a large fly. It means, I suppose, a stream of self-advice -- oh, a bird -- now don't blow it -- slowly-slowly -- oh, how I want to catch that -- I REALLY want to catch it -- I want that more than anything in the world ---
As to cats leaving gifts for the Alpha Cat (that's the human mother/father), there was a period when they did that all the time (under the pillow, under the doormat, on the sink shelf, on the computer table. They stopped putting things in plain sight after a while, because I always gave a highly inappropriate yell of rage and disposed of the gift directly into the garbage can. They also learned not to try to present me with a still living bird or young rabbit or the like, since I always demanded it and took it away -- destination depending on the victim's condition at that point. Cats are clever. They just have their own ideas about what and whom to pay attention to. Anyway, cherish the gifts while you may, because cats figure out pretty quickly that you really think certain kinds of gifts are disgusting.