See http://en.cppreference.com/w/cpp/container/vector/vector example at the bottom for an example of initialization list. std::vector<std::string> words1 {"the", "frogurt", "is", "also", "cursed"}; is an example of the initializator list.
(b.) I think the premise of this question is invalid or ambiguous. sizeof is not used to find the length of the vector, and it also technically isn't a function. vector.size() is what should be used to find the number of elements in a vector. If by "length", you mean the size in bytes of internal data on the heap, you can do my_vector.size() * sizeof(TypeOfMyVector), ex: my_vector.size() * sizeof(int).
For the other questions, you should put some more effort into trying to solve it yourself first, and then come back when you have a specific question.