This paper presents a compact, optical-fiber-free gate driver with nanosecond-scale fault protection for 650 V GaN HEMTs. GaN devices offer the lowest specific on-resistance at low temperatures compared to other devices, making them a desirable solution for cryogenic operation. Conventional isolated gate drivers rely on fiber optics for signal isolation and magnetic-core-based transformers for power isolation, both of which can malfunction under cryogenic conditions. To address these limitations, the presented gate driver eliminates the need for optical fiber and employs a MHz coreless transformer. Also, compact di/dt-based short-circuit and overload protection schemes are integrated by utilizing the small parasitic inductance (Lp) between the Kelvin-source and power-source terminals of a GaN device. This enables ultrafast fault detection within nanoseconds and offers robustness against temperature variations. Although the small Lp and limited current capacity of discrete devices constrain the detection bandwidth and gain, an optimization sequence is introduced to enhance circuit performance. Experimental results validate the effectiveness and robustness of the proposed design.