It's "nazenara", not "nazekara." Those three sentences are all the same, but if you use "nazenara," you should add "kara" at the end of the sentence, like "nazenara niku wo tabenai kara." Ohatsu ni omeni kakarimasu is a kind of greeting as you said. It literally means "I see you for the first time." "Dare mo imasen" is correct, but "dare nimo imasen" is not correct. "Dare nimo iimasen (I won't say it to anybody)" is correct.

1) Here are the literal translations for each sentence. Do you see that they have different constructions while meaning the same? Niku o tabenai kara, raamen wa dame da. (I don't eat meat, so raamen is not good.) Raamen wa dame da, niku wo tabenai kara. (Raamen is not good because I don't eat meat.) Raamen wa dame da. Nazenara niku wo tabenaikara. (Raamen is not good. The reason is because I don't eat mean.) 3) You are almost right. "to issho ni" is actually an adjectival phrase, so it should be followed by a verb. e.g) Watashi wa tomodachi to issho ni raamen wo tabemasu. (I eat ramen together with my friend.) Niku to issho ni yasai wo tabete kudasai. (Please eat vegetable along with meat.) "TO" can be used between two nouns or a noun and a verb. e.g) Watashi wa tomodachi to asobimashita. (I hanged around with my friend.) Niku to yasai wo kaimasu. (I buy meat and vegetable.) If "to" is followed by a verb, in most cases you can use "to issho ni". The examples below are both correct: Watashi wa tomodachi to issho ni asobimashita. Watashi wa tomodachi to asobimashita. I say "in most cases" because there are some sentences that sound weird if you use "to issho ni." Watashi wa anata to kekkon shitai desu. (I want to marry you.) ×Watashi wa anata to issho ni kekkon shitai desu. -incorrect

Btw, how about if you break up your questions to several threads with different titles instead of putting everything into one? It'd be easier to answer and also easier to find afterwards.