Possible problems when 0 bytes remaining

Question

over the past few months I have been getting that "XYZ MB remaining, ... Examine/Ignore" popup screen. Since this is an old ubuntu 10.04 on a small partition, it never troubled me much - after all, the amount it was complaining about was 586MB or such.

But recently I noticed the number has been going down and today I just saw ~180MB and decided to take action. I have a few "housekeeping / space freeing scripts" that i run when I think something's suspicious and that has been keeping me good for now. Today I also ran Computer Janitor and BleachBit to help things out.

Somewhere during bleachbit execution the 0 bytes dialog showed up. My question as a mostly windows user is - if my computer is really down to 0 bytes remaining (opening Desktop shows 668.5MB remaining in the statusbar) is it going to die like any windows machine would? I don't think it would, since it's been running fairly good with a pitifully small amount for a decent amount of time but I'd rather ask than being sorry.

This old ubuntu is really keeping my "skype/email" laptop stable and secure. I would hate losing it or having to update/reinstall anything. I think I actually freed up some space but if it really is down to 0 bytes, I'm kinda scared of restarting the machine. I'm mostly skeptical because gtkdiskfree shows that my /dev/sda5 mounted at "/" has 1.25GB free, while Nautilus shows that it has 668.9MB free, being at the root of "File System"

Please give some useful advice :)

EDIT:
Currently, "df -h" looks like this

shark@DEVSHARK:~$ df -h  
Filesystem            Size  Used Avail Use% Mounted on  
/dev/sda5              12G   11G  1.1G  92% /  
none                  1.5G  344K  1.5G   1% /dev  
none                  1.5G  112K  1.5G   1% /dev/shm  
none                  1.5G  196K  1.5G   1% /var/run  
none                  1.5G     0  1.5G   0% /var/lock  
none                  1.5G     0  1.5G   0% /lib/init/rw  

This is my freespace.sh script I mentioned earlier

#big files  
echo 'Identifying big files...'  
sudo find / -name '*' -size +1G  

#big folders  
echo 'Identifying big folders...'  
sudo du -h --max-depth=1 / | grep '[0-9]G\>'  

#lost trash  
echo 'Identifying lost trash...'  
sudo find / -type d -name '*Trash*' | sudo xargs du -h | sort  

#cleanup packages  
echo 'Cleaning up packages...'  
sudo apt-get clean  
sudo apt-get autoclean  
sudo apt-get autoremove  

#autotrash  
echo 'Autotrash-ing trash...'  
sudo autotrash --min-free=1024  

echo 'I hope you got some free space back.'