how can I download ios 7 manually to be able to get my podcast app back? I am on an iPhone 3Gs with iOS 6.1.6.
Unfortunately  my podcast app has been removed. 
Now, if I want to install it Again, I need iOS 7. However, in my setting for software it states that my software is up to date. 
How can I manually download iOS 7 so that I can get my podcast app back?
Unfortunately the highest supported iOS by an iPhone 3Gs is 6.1.6, you cannot do anything in that regards, the possible solution is to Jailbreak the iPhone and try to get access to Podcast application with that.