This will cause the virtual Machine to Automatically "X"
The notification bubble (small window) you posted above would show you a bit more info if you click on it (not the "X"). The "X" is simply to close the bubble/window. You may have a similar text bubble regarding the auto-capture of the mouse, and you can click on the "X" to close it also. I briefly mentioned these in the instructions (#24) although I called the notification "bubble" a "banner."
OK, I've played a bit now, and a Menu Icon appeared in Accessories on my Start Menu after rebooting my computer (the host computer, not the virtual machine). I installed Manjaro Linux into a virtual machine following the instructions (#6 - #24) that I linked to earlier. The install went fine, except that the default memory of 768 MB was not enough for Manjaro. So I had to start over and give it 1 GB (1024 MB). Also, after installing, it seemed to continue booting on the .iso file (in the "storage" section)... so I shut it down, went back into Settings/Storage and deleted the .iso (right-click on it and delete attachment) and then it booted properly on the installed virtual machine. It all seems to run okay now.
Some items to consider...
1. Let us know what Linux you are trying to install. That may make a difference... some may not work well in VirtualBox.
2. Did you "verify" the .iso file that you downloaded? That was step #4 in the instructions, but that person was using Windows. It is really a good idea to always verify a Linux .iso file to be sure that it is complete and not corrupted. If you install an operating system from a bad download, all kinds of things can be wrong with it (if it even boots at all... which yours is not right now, or so it seems). I don't remember if we've covered this step with you yet or not, so if you have any questions about how to verify the .iso just ask. Linux Mint has the tool built-in that you need to do this, but we need to know which Linux you are trying to install.... including whether 32-bit or 64-bit versions.
3. When first beginning with VirtualBox (steps #7 - #9 of the instructions)... you give the virtual machine a name, then select whether Windows or Linux, and then select a "version" of Linux. These are all on the same screen. The "version" should match what you are installing, or at least be close. The instructions I gave say to use Ubuntu as the version for Mint because Mint is based on Ubuntu. On my install today, I picked Arch Linux as the version because Manjaro is based on Arch. This is a possible source of trouble for you.
4. Freezing? I just want to try to make sure of this situation. Those notification bubbles about "auto capture" of your keyboard and mouse might be a clue to this problem. When a virtual machine is running.... the mouse and keyboard need to respond to commands from BOTH operating systems. This can be confusing, and different computers may handle this situation better than others. I noticed at times that if I moved my mouse into the Manjaro virtual machine "window"... that the mouse cursor would disappear. After installing and everything settling down it seems to work okay now, and the mouse works in both Manjaro and Mint seamlessly. But VirtualBox does provide a kind of fix if this is a problem... it probably shows in the lower right corner of the virtual machine window and says,
"Right Ctrl"... meaning the right-hand Control key on the keyboard may help to restore mouse and/or keyboard function. Honestly, I'm not quite sure how it works because I've had good luck with VirtualBox and not too many troubles.
5. I did not go back and re-read this thread, but let's also confirm those 32-bit and 64-bit questions while we're trying to consider if you have a problem or not. If your Linux Mint is 64-bit... you
MAY can run a 32-bit virtual machine, but I am not sure. If your Linux Mint is 32-bit, I am almost certain that it will not run a 64-bit virtual machine. Mixing these system specs is just a potential reason that you are having trouble with your install.
A number of things for you to consider, so let us know a bit more and we'll try to help you along. I'll be happy to install the same distros into VirtualBox that you are trying, but we still may have different degrees of success since we're using different computers.
Cheers