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They are replacement screws to replace the 2 pentalobe screws that you removed in the first step. Because these screws are designed to prevent tampering, they are easy to strip and Apple replaces them when they remove them (if I remember correctly). The battery kit comes with 2 replacement screws that are philips head instead of pentalobe so a special screw driver isn't needed for future repairs.
It will probably not make a click noise. It should push on and be "stuck" when seated. It shouldn't move easily and should be level. If it is not level, or is still free when you touch it, it is not attached properly.
I bought the iFixIt kit to go along with the battery. It was a big help mostly because of the tweezers that come with it. I got 1 adhesive strip off okay, but the 2nd snapped and hid under the battery. By prying the side of the battery up slightly and using those tweezers, I was able to get a hold of the adhesive strip and pull it out. It ripped a few more times, but I managed to get it out without bending the battery too much. I also left the display attached, by propping it up against a heavy box and holding down the iphone with a lot of pressure (on the sides to avoid hurting any internal componenets). I would definitly recommend beginners DO NOT do that, as those ahesive strips take a lot of effort to get out and it would be easy to slip and rip the cables. If it weren't for the adhesive, I'd say it is pretty easy to just leave the display attached.