Wikipedia:Policies and guidelines describes how Wikipedia arrives at its policies and guidelines through a process of discussion and consensus. Discussion takes place in the various policy pages which form part of the "Wikipedia:" namespace. Sometimes policy is discussed off-wiki, but decisions always take place on-wiki.
Two words for the same thing. An administrator is simply a Wikipedian who can access some of the few restricted Wikipedia software functions: deleting articles and uploaded files, protecting and unprotecting pages, and blocking and unblocking users or IP addresses. The software internally uses the string "sysop" to flag their accounts, perhaps one reason that term is used. "Sysop" is simply a shortened term for system operator. They tend to be friendly folks who are willing to help you, if you post on their talk page. See the current list of administrators.
In short, you spend years developing a good edit history that shows you understand Wikipedia policies, have good judgement, a good temperament, and have a need for the administrator toolset. A nomination is then made at WP:RFA where the community decides if the user merits the tools. Administrators have no special status and are like any other editor, they simply have tools that would be irresponsible for the entire community to have. You can do probably 95% of tasks on Wikipedia without being an administrator.
Only administrators can unblock IP addresses. Developers can unblock multiple IPs at once. To request that an IP address be unblocked, see Wikipedia:Appealing a block and follow the instructions there.
How can I request for an admin to block a user or IP?
You can request for an administrator to block a user or IP that is blatantly vandalising at WP:AIV (see requirements on that page). More complex cases can be presented at WP:AN/I.