I need to move my computor from one side of the room to another. Do I need to close everything and shut it down first?
Doing this is a good idea, however if the power cable is long enough and you are using an SSD you can move it while its on.
The main risks are -
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You will dislodge the power cable causing a sudden shutdown and risk some data loss. With modern systems and journaling filesystems this risk is very small - same risk if you don't have a UPS and there is a power outage.
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if you have an old style spinning hard drive you are risking damaging it because of extra vibration/knocks while it us spinning. There is a risk of permanent data loss. The risk is not massive but not negligible either. This risk does not apply to SSD's as they don't have moving parts.
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There us a risk if dislodging a cable, which could cause a confused state This risk us not much higher then the risks of knocking out the power cable.