Should I restart when prompted?
Yes, you should. For most cases, a restart is required when an update to the Linux kernel has been installed. These updates are usually security updates, and then only come into effect after a reboot. Updates to normal applications such as Firefox come into effect after you restart the program. Firefox should prompt you to do this automatically, but other programs may not, so it's something to bear in mind.
How to restart:
To restart the computer in Ubuntu 21.04, click the power icon in the upper right corner of the screen, and select "Power Off/Log out". In the sub-menu that appears, click "Restart...".
To restart from the command-line, run this command:
$ sudo reboot
The downsides of restarting:
On the whole, restarting is a very safe operation, and I would not consider it in any way unsafe. Of course, when you restart the computer, you lose all the information in RAM, so make sure you save all open documents and files before shutting down your computer. While you are restarting, your computer will of course be offline for a few minutes. If you're running a server, it will be down for a few minutes. If you have an open SSH session, it will be terminated.