Is extra hardware and components needed to connect the bare MCU directly to a PCB, without a shield?
DO I need crystals, capacitors, etc? Or the MCUs (mostly AtMega 32u4 and Attiny85 and Attiny167) have it all what's needed inside them?

You don't need a crystal if you use the internal clock of the MCU (which means setting the fuses right and compiling your code to expect the right clock frequency). However if you are using a direct USB interface (such as for the ATMega32U4) then you will need a crystal as the precise timing is required for USB to operate.
You will need capacitors. Decoupling capacitors on all the power pins are not optional and must be included.
You will need a pullup resistor on the RESET pin unless you have set the fuse to disable the RESET pin (not advisable since it will prevent ICSP programming in the future - but can be useful for low pin-count chips).