stuck home button, stuck home button

Try:

http://snapguide.com/guides/calibrate-your-home-button/?utm_expid=69945963-15

fix for Home button

iPhone Home Button Not Working or Unresponsive? Try This Fix

- If you have iOS 5 and later you can turn on Assistive Touch it add the Home and other buttons to the iPods screen. Settings>General>Accessibility>Assistive Touch

- If not under warranty Apple will exchange your iPod for a refurbished one for:

Apple - Support - iPod - Repair pricing

You can do it an an Apple store by:

Apple Retail Store - Genius Bar

or sent it in to Apple. See:

Apple - Support - iPod - Service FAQ

- There are third-party places like the following that will repair the Home button. Google for more.

iPhone Repair, Service & Parts: iPod Touch, iPad, MacBook Pro Screens

You also said "

2. Will IOS7 take up more space and slow down the operation of above iPod Touch?

Only the 5G iPod (and some iPad and iPhones) are cmpatible with iOS 7. The 1G iPod can only go as hig as iOS 3.1.3

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