1: Yes, it is grammatically correct. Although it sounds a little awkward to repeat the topic. Perhaps ...the most influential study in the area. 3: Yes, sure, in general. But not in the example you gave. 4: It is grammatically correct, but not very natural. We would normally use 'noting' instead. I would perhaps use 'noticing' only for a visual feature, such as a feature of a picture, or a graph. Your quote there "cultural...dimension" is not grammatically correct though, and I'm not sure what you mean. 5: It would depend on the timing. Were the studies written before, or after Ting-Toomey?

1. Is this sentence grammatically correct? Did I use punctuation correctly? “It reviews Brown and Levinson’s face work theory; the most influential facework theory.” (First, it is unclear what kind of theory you are talking about. I do not recognize that word. Second, you need a semicolon because these are two separate, but well connected ideas.) 2. If the above sentence is incorrect, can you help me to correct it, please? 3. Can I put ‘thus’ in the sentence like this: Clause 1 and, thus, Clause 2. Is this correct? (You can only sometimes have "thus" surrounded by two clauses. She hates grammar, thus making grammar lessons useless. It is better to make clause one its own sentence. She hates grammar lessons. Thus, grammar lessons are useless. Either example is correct, but the second might be easier to remember because the tenses are mixed in the first one.) 4. Is this structured correctly: It is worth noticing that +Cl. e.g. It is worth noticing that “the cultural variability dimension of individualism- collectivism is not a static dimension.” 5. Should I use present tense or past tense for this sentence: “There are several studies providing supportive evidence for Ting-Toomey& Kurogi(1998)’s face-negotiation theory.” (You should either use present tense or present perfect tense for this. For example: there have been several studies which provide.)

1) The sentence is correct. I will say, depending on the context, you may want to break that into two sentences to help it flow better. “It will review Brown and Levinson’s facework theory. Theirs is the most influential facework theory to date.” or something similar. 3) Yes. In this case, "thus" would work the same as "therefore" or "and so". 4) The structure is correct. 5) Present tense is best. This seems like a formal paper, so unless you're specifically relating a sequence of events that occurred in the past, it's best to stick to the present tense.