I'm not familiar with the EQ in Reason, but to explain the mentioned "elements", or filters in the EQ:
- Lowpass filter, cuts everything above the frequency you've set it to (sometimes also called a high cut)
- Highpass filter, same as above, but cuts everything below (sometimes also called a low cut)
- Bells (also called Peaks, which is more common to my experience), simply the standard EQ shape, you boost a frequency, and the shape of it looks like a peak with slopes on the sides.
- Don't know what you refer to with the low-mid-high-etc EQ's (the first 4 shapes you mention), but I suppose they mean the locations of 4 peak/bell shapes.
- The spectrum, I mean if you don't understand that yet, is the whole area of frequencies that us human beings can hear (20 Hz - 20 kHz).
Anyway, what I mean with sweeping a peak through the spectrum, is simply boosting an EQ spot (that is a peak or bell shape), and then sweeping it up and down on the EQ to more easily find spots that sound horrible, or spots that simply makes the sound sound better when it's boosted. This way it's easier to detect what you need to do to a sound.
This is a common habit, and applies to all instuments as uses for an EQ.
So boost a place on the EQ, and move it across the EQ very slowly, and you'll hear if a certain place sounds pretty worse when it's boosted, then you know you need to cut it a bit.
Then as I mentioned, you can adjust how wide the boost is, from covering a huge range of the spectrum, to covering only 1 frequency at a time. By sweeping on the EQ with different widths on the boost, you can both find horrible bigger areas on the EQ that you want to cut, as well as finding horrible specific frequencies that sound really bad.
And what I mean with the number ca +6 dB, is that if you use a less boost than that, it can be a bit hard to hear wether a certain area really is worse when sweeping up and down, while a much bigger boost is more likely to sound bad all over the place, making the process completely pointless. This number however is from my own experience, some people may prefer a bigger or more gentle boost, but for me this is the boost I usually go for (to be more exact it's more like +6 dB-9 dB).
I hope this makes a little more sense.