Computers for 24/7 operation-should they be shut down periodically?

There is no hard and fast rule as to how often you should shut your computer down or how long you can keep it running continuously. Most computers when idle, automatically go into low power mode or sleep mode, which cuts down on power usage and heat.

I run a small home business and I have a home server that has been running 3 weeks continuously without any problems. I only power it down occasionally to do some cleaning (remove dust) or when I need to perform some upgrades, but otherwise, it's always on full time.

I would think the hotel's IT department would be the best to ask about that.

For my home office, I shut my computers down for a couple of minutes every 3 or 4 days, then reboot, do my maintenance (disk cleaner, CC cleaner) etc.

They should only be shut down if you want them to be. Its fine to leave them up, but an occasional reboot, like during updates, isn't a bad idea.

yeah its ok but you can reboot from time to time just for update to work