Is it possible to use all the outputs from a power supply at the same time?
Yes, that's why it has more than 1 output. 

Sanity check : it's a 60W supply but the 5V rail is only 30W (6A) and the 24V rail is rated 1.2A (also 30W). Note the 12V rail is rated at 1.5A (18W) so there may be restrictions on using all 3 outputs at full power.

Also check : is 1.2A enough for the motor you are using on that 24V rail? Motors tend to take quite high currents when starting : that can trip the protection on some designs of power supply.