If I have a hard disk with more than 50% free space, will it become slower if I consume 30% more disk space? Why or why not? It never made sense to me that more free disk space would equal better performance as long as programs aren't running in the background and Windows or Linux doesn't need the extra disk space for a cache. Would a hard drive with more free disk space boot up faster? (I can understand that defragging could help, but what about free disk space in general?)

I think the only issue here is the swap file.
Windows needs approximately 15% free space to function efficiently.
This issue confuses many people, but as far as I can tell, you are correct:Installed programs don't affect performance unless they have some memory resident component.