We introduce a comprehensive approach to enhance the security, privacy, and sensing capabilities of integrated sensing and communications (ISAC) systems by leveraging random frequency agility (RFA) and random pulse repetition interval (PRI) agility (RPA) techniques. The combination of these techniques, which we refer to collectively as random frequency and PRI agility (RFPA), with channel reciprocity-based key generation (CRKG) obfuscates both Doppler frequency and PRIs, significantly hindering the chances that passive adversaries can successfully estimate radar parameters. In addition, a hybrid information embedding method integrating amplitude shift keying (ASK), phase shift keying (PSK), index modulation (IM), and spatial modulation (SM) is incorporated to increase the achievable bit rate of the system significantly. Next, a sparse-matched filter receiver design is proposed to efficiently decode the embedded information with a low bit error rate (BER). Finally, a novel RFPA-based secret generation scheme using CRKG ensures secure code creation without a coordinating authority. The improved range and velocity estimation and reduced clutter effects achieved with the method are demonstrated via the evaluation of the ambiguity function (AF) of the proposed waveforms.