where is podcasts in my iphone 5s?

l use to always listen to my many podcasts in my iphone, they were set up to sync with my mbpr itunes. the mbpr still has the many podcasts but it doesnt even seem to exist in my iphone. l thought it might of been uninstalled so tried downloading it again from my app store, but it seems l still have it in my phone, as it shows "open" rather than "get", as it would if l didnt have. the problem is when l click on open, nothing happens, the "podcasts" icon is not there in any of the pages. where is it?

my sister also has an ipad with the same podcast software, but nil podcasts, how can l get my podcasts on this ipad? when l connect it to my mbpr, itunes asks me : "set up as a new ipad" or "Restore from this backup: "applet iPad" , which option will keep all software downloaded and just sync only my podcasts to the podcast software that is already on the ipad, with no interference with anything else?

Hi Applet,

Podcasts is now a Native iOS App. Meaning, it comes as a installed App, rather than you having to download it.
What you need to do, is goto your Home Screen, and swipe down to bring up Spotlight. Type Podcasts into the Search Bar, and tell us what comes up. IF, you have iOS 8 installed, it should chomp as the top hit. If it does, tap it, and it should open. If not, I would try restarting your iPhone, or do a Hard Reset, by holding Top Button and Home button at the same time, until the screen goes Black. Once you see the progress indicator disappear, start it up again, and go through the process of searching and opening again.

IF, this doesn't help, I would give Apple a call, or go into them, and see if they can't install iOS again.

As too getting your Podcasts on your Sisters iPad, that won't happen, unless you setup as a New iPad. The reason being, is, its now synced to your sisters Apple ID, and for you too sync it, you need to set it as a New iPad, and use your Apple ID to set it up.
You could get your sister to subscribe to the Podcasts you need until you can sort the issue out on your iPhone.