The RISC-V core is a custom design. It supports the RV32-IMC extensions. More details about the CPU will be published in the ESP32-C3 Technical Reference Manual which is currently being finalised, thanks for being patient.
The "factory maker" for all Espressif chips to date is TSMC, Espressif is a fabless semiconductor company which means we design our own chips but the silicon is fabricated by a third party foundry.