Half of the time when I first open Opera 25.0.1614.68 (OS: Yosemite), doesn't matter if I select a link through speed-dial or just type in an URL; Opera will just hang there until I quit the programme. When I restart Opera, I can click on a speed-dial link or type in an URL and it will work perfectly. This is happening on my mother's DELL laptop as well (which is running Windows Vista).
Please correct this issue.
P.S., I've deleted and re-installed Opera twice on both computers, hoping the issue would be corrected, with no avail.

Never had this issue. On any computer. Do you have any third party addons/extensions installed? If so, could you try to uninstall everything and try again?