Are these lens compatible with Nikon D5100?

AF-S DX Nikkor 18-55mm f/3.5-5.6 G VR? Also, would these be their kit-lens?

Yes. All Nikkor AF-S lenses are compatible with the D5100

The 18-55 is the "kit lens"

Here is a link to all the current Nikkor lens

http://www.nikonusa.com/...index.page

That is Nikon kit lens. As far as other older Nikon lenses go, compatible - yes. Do they have enough resolution and clarity to support a large megapixel sensor? Probably not.

This is the standard kit lens for the D5100. As for other compatible lenses, you need an AF-S lens with built-in autofocus motor or comparable Sigma HSM, Tokina, or Tamron optics.

Here's a current list of fully compatible lenses.
http://en.wikipedia.org/...cus_motors

All nikon F-mount lenses will mount, and different generations have various levels of compatibility.
http://www.kenrockwell.com/...y-lens.htm

It's only one lens and it's the kit lens for the D5100. Yes it is fully compatible in all aspects.