Is it possible to increase the root filesystem size without reboot ??
No....!!!!
I don't think you can resize Root File System.So, no question of reboot.
You should plan it (size) correctly during O.S installation keeping future requirements in mind.
With several restrictions, you can resize the root file system but you need an different bootable media and to reboot a couple of times to achieve that.
Without reboot is not possible ??
thats what they told you with their answers...