Working with Frame Rates & Slow Motion in Adobe Premiere
To answer your Questions in order:


You can see the framerate of a clip or sequence by navigating to the metadata panel. It's usually one of the tabs in the upper left on the standard layout. If you don't see it, select Window -> Metadata.
Generally, you should set sequences to match you source material. So if your camera records 720p @ 60 fps, stick to that. You can review and change the sequence settings under Sequence -> Sequence settings. Some settings can't be changed later on though.
The best way to create a slowmotion effect is to use "time remapping". You will find that under the effect settings that every clip has by default. There you will see that your clip has a standard speed of 100%. You can change the speed of the entire clip by altering that value. If you want the clip to gradually slow down over time, you'll have to use keyframes. You can set a keyframe by clicking on the square symbol in the effects panel next to the time remapping line.
In this case, you'll need to create two keyframes, one at the beginning and one at the end of the transition from fast to slow. Let the first keyframe at 100 % speed and set the second to your desired target value, for example 50 % and that's it.
I hope this was somewhat understandable. If not, it's futher detailed at the adobe help site: http://helpx.adobe.com/premiere-pro/using/duration-speed.html
Can't really help you with that. If you're going for real slow slowmotion, you can always right-click on the clip and activate frame blending, which might result in a smoother video.


I hope i could help :)