Why do flouresant lights flicker and seem to lose power when other appliances turn on or just dont want to power up themselves?

What you are seeing is voltage drop. This condition happens when there are too many appliances connected to one circuit. This is one of the reason that code requires separate circuits for appliance circuits. When they don't want to power up it is a good sign that it is time to replace the tubes. If you see dark black marks at the ends of the tubes that is a sure sign to change them.