• Attach the hair by first positioning it correctly on the figure. Now with it still selected go to Object/Properties (ctrl+i) and click the "Set Parent" button. Select the head. As an alternative for long hair try parenting to the neck and check the "Inherit bends" box.
• To get a higher resolution when rendering go to Render/Render Options (ctrl+y) select New Window and fill in the Resolution box to your requirements.
• To remove that unwanted hair simply click on it to select it and hit the delete key.

Hope this all helps :)