I'm not an expert on lenses so maybe someone else can give more info but the answer to your question is yes and no. If the lens starts at 3.5 at it's biggest opening, when you zoom in on a subject the value increases, this is what I'm not sure about as to why. It's something to do with the lens design.
Most of my lenses are pro lenses and are 2.8 all the way through so on my 70-200mm I set my aperture to 2.8 but when I zoom in the aperture stays at 2.8. These lenses are commonly referred to as fast lenses and are great in low light conditions such as indoors as 2.8 will let in a lot more light than say 5.6, 8, 11 etc.. and this is why they cost so much
You are right regarding the effects and in this case the effect will be Depth Of Field. DOF at 2.8 for example is quite narrow, so when you have focused on the subject, what the lens sees in front and behind is then blurred and how much depends on your focal length. The reason it is blurred is because the big opening of 2.8 will send a splash of light to the cameras sensor but because it's a splash of light it's not able to capture the detail in front and behind the subject hence the blurring.
To capture more detail in front and behind the subject, you'll need to increase the aperture size. As the numbers increase, the hole gets smaller so light is more gradually allowed on the censor so it captures more detail. This is why around f18 is used commonly used by landscape photographers as the detail is captured from right in front of the camera right into the distance with no blurring.
That's a quick overview but pictures especially videos speak louder than words. Here is another video I've found on youtube for you:
YouTube - Photography tutorial - depth of field
You'd be amazed of the video resource that's available on youtube and it's worth looking on there for any photography tutorials.
Hope this helps.