Is the Nikon D3100 a 35 mm digital single lens reflex?

Also, what lenses will have an adjustable shutter and an adjustable aperture?

Yes. All of them. The shutter is in the camera body. All lenses for DSLR's are adjustable aperture. The maximum aperture varies by lens.

Actually there's no such thing as a 35mm digital camera except that some sensors are what's called full size at 35mm. 35mm is a film size.

The 3100 is a digital camera and yes, it's full adjustable

35mm is a film with a frame size measuring 24mm x 36mm. The Nikon D3100 has a digital sensor that is smaller than a 35mm film frame (24mm x 36) and has a "crop factor" of 1.5x. A full-frame DSLR like the Nikon D700 or D3 has a digital sensor that measures 24mm x 36mm - the same size as a 35mm film frame.

No lens for a DSLR has a shutter. The shutter is contained within the camera body. Lenses have an internal diaphragm that consists of a number of movable blades that form the aperture opening. The aperture is controlled by selecting the aperture desired on the camera controls. In the old days lenses had an aperture ring on the lens barrel and we used that to select the desired aperture.

Spending time at these sites will really help you:

http://www.digital-photography-school.com
http://www.cambridgeincolor.com
http://www.kamerasimulator.se/eng/?page_id=2
http://www.illustratedphotography.com/photography-tips/basic

Technically speaking, not 35mm. It is a DSLR but only full frame and film cameras are 35mm. That's the least you have to know right now.

All DSLRs can control the aperture as all lenses have it, and all cameras have shutter speed control.

Here's a DSLR Buying Guide - http://www.the-dslr-photographer.com/2009/11/which-dslr-to-buy/