Is it possible to switch between different Linux distributions without restarting? For example I've installed Ubuntu and Arch Linux multi-boot. And I want to switch between them without restarting my computer.
It is technically possible, but not neccessarily practical.
The "cheat" way to do this would to run each distro in a VM, and switch between VMs. Most testers would use a variant of this.
It might be technically possible to create a chroot jail and set up a second distro in a directory of the primary OS and then "pivot" to it and restart apps, but this would be messy and cause residual issues, and assumes compatible kernels and fairly in-depth knowledge of everything. (I note that Crouton uses this technology to run Ubuntu in a Chromebook, so its doable in theory)
Yes you can, using VMs. I have dont the following in one direction, booting Windows, then loading Mint from another hard drive into a VM. Using VirtualBox and its raw disk option you should be able to boot one OS inside the other. I dont see why you cant do it the other way around as well, booting from the second OS and launching a VM of the first OS. However, it might take some work.