What is the best way to limit the time of use of iPad 4? I have iPad 4 with iOS 8.2. Also, I have a child. I want to set some time limit (per day) of use of iPad for my child. 

Also, I want to have some profiles or something like that. Other words, I want to have time limit on Profile 1, but I don't want time limitation on other profiles, which have to protect by password.
Sorry but iPads (and iPhones) aren't intended to be used as multi-user devices. At least not like you mean with different profiles like you would find in Windows devices or recent version of Android.

The closest thing on iOS devices is Guided Access, where you can lock the device to a particular application and specify time limits. You need to enable it in "Settings > General > Accessibility > Guided Access" choosing a password and turning on the Accessibility shortcut which allows you to bring up the Guided Access feature by triple clicking the Home button. Then you open the app you want to lock the device to, triple-click the Home button and it will allow you to specify time limits, and allow you to enable or disable certain parts of the device. Then click Start.

You can read more about Guided Access on Apple's website here.

There are other third party applications that promise to offer similar features, you might want to investigate them. Of the ones I looked at none stood out and the reviews didn't inspire confidence.