1) The definite article is not necessary in these kinds of contexts. In documentation of this sort, you'll see both "a user makes a request" and "the user makes a request," since you're speaking of a hypothetical user. Of course, if you defined a narrower subset of users and were speaking about them, you'd need the direct article: "Users can log in and after they've done so, the users can view their account."
2) It's optional, and to my ear, sounds worse. I prefer "user requests," which puts the focus a little more on the request than on the user (and the system performs differently because of the requests, not because of the users). It's a subtle distinction, though.
3) "Users requests" is not a form that you would ordinarily see, but it's grammatically valid. Users requests would be the plural of users request. A users request would be a single request that is made by a group of users (for instance, a group of users vote on which request they want to make), or more likely, it might be a request for multiple users - i.e. not a request made by the users, but a request made by someone who wanted users.
Remember that attributive nouns, like the adjectives they resemble, or function as, are not pluralized, unlike some other languages.
One user request => two user requests NOT two users requests
One mouse trap => two mouse traps NOT two mice traps
Also note that some attributive nouns are always plural.
One sales manager => two sales managers
One singles bar => two singles bars
What determines whether an attribute noun should be plural or singular? Unfortunately, it seems there's no clear answer. This article is insightful: "Why isn’t it a gumsballs machine?"