Hi all, do all ASICs have both RAM and CPU (microprocessor), do all normal integrated circuits have both RAM and CPU?

no and no

ASIC: Application-specific integrated circuit is an integrated circuit (IC) chip customized for a particular use, rather than intended for general-purpose use. While many do include RAM and CPU, many are just combinations of digital and analog ICs.

normal ICs include logic ICs, opamps, regulators, etc, none of which contain RAM and CPU.

wikipedia:As feature sizes have shrunk and design tools improved over the years, the maximum complexity (and hence functionality) possible in an ASIC has grown from 5,000 logic gates to over 100 million. Modern ASICs often include entire microprocessors, memory blocks including ROM, RAM, EEPROM, flash memory and other large building blocks. Such an ASIC is often termed a SoC (system-on-chip). Designers of digital ASICs often use a hardware description language (HDL), such as Verilog or VHDL, to describe the functionality of ASICs.