Why is my iPod running slow, uses nearly 600MB of space that I'm not using, and have short battery life?

I have owned an iPod touch for about a month now and I having some problems with it. On occasion, my iPod is running very slowly, even when I keep my multitasking bar empty, the native apps such as the App Store, Music, Videos, etc. lag a lot whenever i try to access content. This was not the case for me when I was running iOS 4, in which my iPod ran extremely fast and had great battery life. I most of the time keep my wireless turned off (to be specific, i turn on airplane mode approx 3/4 of the time) along with my brightness turned all the way down. Any suggestions?

I also have another concern with my storage space. I have an 8GB 4th Generation, and whenever I plug it into iTunes, I notice nearly 700MB of space that I am not using on my iPod, I have gone through all of the data and calculated that the 700MB of space that iTunes classifies as "other", i am not using this storage space. Is there anything that I can do about this or do I have to erase everything and restore to get rid of this?

Thank you for taking the time to read my question, and if you can, please answer.

Thanks.