Quite frankly, unless a person is an attorney, in your state, who is willing to give legal advice, without facts, or compensation, no one can really answer "what it means".
That particular Rule 287 of the Illinois Supreme Court Rules means that pre-trial discovery in small claims is conditioned upon the prior approval of the small claims court. “Leave of court” thus means “permission of the court” granted upon a showing of special need or good cause.
“Requests to admit” as used in the Rule is a reference to a common form of pretrial discovery known as “Requests for Admission” in which the opponent is asked to either admit or deny (usually) a series of composed statements of the factual issues in the case. Generally for the purposes of narrowing the disputed issues and saving time in trial preparation and trial. If neither denied or admitted, they are deemed admitted.
Here, because prior permission is required it seems reasonable to assume that the defendant received that permission before submitting the discovery requests.
And inasmuch as attorneys are permitted to practice in Illinois small claims case, it is very likely that the defendant has employed counsel who prepared the discovery requests.
Also, it is deemed most irresponsible for anyone to suggest that the OP ignore the defendant’s discovery and thus be subjected to a host of court sanctions, including, among other unpleasant orders, having his or her complaint dismissed with prejudice and assessed the defendant’s court costs and possibly the defendant’s attorney fees in seeking such sanctions.
If the OP wishes to submit discovery to the defendant, then he or she should avail under Rule 287 and make a similar request to the court.
Now whether the OP is capable doing that and preparing and submitting discovery material in the form and within the directives of applicable Court Rules is another issue. But I don’t think it unlikely.
Plus I think Illinois’ Rule 287, and permitting lawyers to practice in small claims, defeats the very purpose of small case litigation as generally understood to be designed to provide a less formal and less expensive adversarial setting.