The valid argument forms and the existential quantifiers can appear anywhere on the LSAT, not only in particular types of questions. Sure, they may appear more frequently in certain types of questions, but it's not a hard and fast rule.
>>1. Does everyone generally set up global diagram on the first page and draw out the rest of local diagrams on the next page as the questions come up?
Yes. Do the "global" on the first page and "local" for individual questions as ...