See if any of these suggestions help.
Quit the Safari app completely and restart the iPad. Go to the home screen first by tapping the home button. Double tap the home button and the task bar will appear with all of your recent/open apps displayed at the bottom. Tap and hold down on any app icon until it begins to wiggle. Tap the minus sign in the upper left corner of the app that you want to close. Tap the home button or anywhere above the task bar. Restart the iPad.
Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.
Go to Settings>Safari>Clear History, Cookies and Data. Restart the iPad.
The problem still goes on. After clearing the browsing history and cookies and reboot then iPad mini, the safari works again. The operation in the web page (ie: touch the link in web page or enter something in the web page) is normal. Touching the upper left corner arrow heads and bookmarks can do normal reaction.
But if I touch (only touch) the web address entry column or the search column of the safari, the browser just be frozen ( the browser should open the keyboard to let me input something but it does not do it)
This situation I faced is the same as using iPad 2. I solved this problem already in iPad 2. If I restore the iPad 2 to default setting, the safari can really work normally. But if I reinstall all previous apps, the safari will be abnormal as the above situation. Therefore I found that if I just install some apps I need and not including all previous apps, the safari can keep to work normally. The not reinstalled apps include many game apps. Is the problem coming from game apps?
Three days ago, I installed one action game in my iPad mini and run it only once time. Two days ago, I found the safari worked abnormally. At that moment , I thought the problem may be from the game app so that I deleted the game app immediately. But now the safari of my iPad mini still has the above problem. what I think is to restore the iPad to default setting with connecting to iTunes in my Mac computer and then the safari will become really normal again.
But can I have another method to restore only the safari and not the whole iPad again as all other apps including other web browser I installed are working normally.
I might have a solution to your problem, my new ipad Mini was having some of the same issues. I finally went into Safari menu in the Settings app and turned on "Always Show Bookmarks Bar" switch, which adds the bookmarks bar below the navigation buttons in Safari and I discovered that I was able get the address bar and search bars to respond normally after I did that. Hope this helps you.