'Since' can sometimes carry the meaning 'because', as well as sometimes being strictly time-based. Sentence #6 of yours is the best example of this - both clauses are in the same time period and it's interpreted that your health is bad because you are smoking. However, intentional or not, some of your other sentences carry this meaning. I would interpret your sentences as follows: 1. I haven't heard from her since she has lived in London. -- Because she lived in London, I haven't heard from her. (? Maybe you got in a fight because you found out she once lived in London? The sentence makes little sense.) 2. I haven't heard from her since she lived in London. -- She used to live in London, and now no longer lives in London. I talked to her while she was in London, or before that point, but not after. 3. I have been in poor health since I have smoked cigarettes. -- It is the case that I have been unhealthy, and this was because I smoked cigarettes. (It is unclear if you are still unhealthy, only that you once were). 4. I haven't heard from her since she was living in London. -- She was in London, and it is possible that I talked to her then, but now I don't. 5. I haven't heard from her since she has been living in London. -- You haven't heard from her because she is currently living in London. 6. I have been in poor health since I have been smoking cigarettes. If you want to force 'since' to refer to time and not cause, we can instead say 'ever since'. In some of these examples this breaks the sentence, but in some it makes it a lot clearer. "I have been unhealthy ever since I started smoking" -- I started smoking, and from that time onwards, I have been unhealthy. "I have not heard from her ever since she lived in London" -- she lived in London, and then I stopped hearing from her.

Although the grammar books say that you can use the present perfect tense after since, I still think that the formulation in sentence one sounds very unnatural and is not something that a native speaker would ever really say. The formulation in sentence 5, where one could say "I haven't heard from her since she's been living in London," i.e the present perfect continuous sounds better and is something that a native might say although, as has been said before in this debate, most people would use "since," with a one-off event in this type of sentence and would instead say "I haven't heard from her since she moved to London." I agree with Zach that the formulation "ever since," helps to remove any lack of clarity in meaning from these sentences. "I've been in poor health ever since I started to smoke," for example.

If you are trying to use "since" in the temporal sense, you should be saying something like: - I haven't heard from her since she left London. (or, moved away from London) - I haven't heard from her since she moved to London. - I have been in poor health since I started smoking cigarettes. "I have been in poor health since I began to smoke." This means that you have been in poor health BECAUSE you began smoking. If you replace "since" with "because" you can probably understand it better: "I have been in poor health because I began to smoke." If you want to say that you have been in poor health from the time you started smoking, you should say something like: "I have been in poor health ever since I started smoking"

I can't understand your question especially when you ask if it is bad or good to use some grammar tenses. There are certain rules of the English grammar and everybody must strictly follow these rules. Only three tenses can be used after "since" - The Past Simple, The Present Perfect and The Present Perfect Continuous. That's all. You used The Past Continuous in one of your sentences - I haven't heard from her since she was living in London. It's completely wrong. The Past Simple is used after "since" when the action is finished, completed. I haven't heard from him since he left for Chile. My friend hasn't smoked since he graduated from the University. The Present Perfect Continuopus is used when the action is still going on. She has been happy since she has been living in Italy. I have been in poor health since I have been smoking cigarettes. The Present Perfect is used after "since" when the action is still going on but the verb is not used in Continuous.