We don't know what version of the Mac OS you have but, in some and depending on how you check for space, there is a reporting error about free space until the Spotlight database is reindexed. If you are checking free space via "About this Mac" you can encounter the bug. To be sure you are seeing a true picture, highlight your hard drive icon by single-clicking it and then do the key combo command i. That will display this window:
Do the lines I've highlighted in red show more "Available" space?
As for the battery, please do this: inside your Applications folder is a Utilities folder. Inside that find either "System Information" or "System Profier" (the name depends on the Mac OSX version) and launch it. When its window is showing, look in the left-hand contents pane for "Power" and click it. The main pane will change to look something like this--the red rectangle is something I added to the image for emphasis:
On your computer, highlight the lines I've outlined in red, then copy and paste that information into a reply to this thread. That will give us an idea of your battery's actual condition.
