I saw two videos where this sensor is connected probably to a Nano with no resistors:
over SPI
over I2C
Is this possibility or is it a bad practice? Or will it work just for a 3.3V Nano?
The ADXL345 is a 3.3V device. Connect it directly to a 3.3V MCU or use level shifters with a 5V MCU.
It may work for a while, connected directly to a 5V MCU, but you will eventually end up with dead chips.