Well, basically it's correct that the C Major chord is made up of the tones C, E and G. On a usual guitar, when you strum the "normal" C chord (not the barré one) and omit the low E string, the following tones sound: C E G C E. So that's five distinct tones ringing, but actually only 3 really different ones, yet in different octaves.
Your're right, the C7 chord requires the tone Bb to create a "minor seventh" chord (that's what the "7" means); the "minor seventh" tone is always 1 full tone below the octave above a base tone, so for the C tone, the "minor seventh" tone is the Bb above it.
When trying to play that on a guitar, the best choice is to put a finger on 3rd fret of the G string, so tone Bb rings. When you now strum, omitting the low E string, the following tones sound: C E Bb C E. As you see, there's no G in it. The G is the fifth (interval) tone above the C, and as others already commented, not so very important for the character of a chord (it makes it only more "bold" or "fat").
On a guitar, you always depend on how you can best put your fingers onto the neck.
Seventh chord and keys
Of course you won't usually see a C7 chord in a song which is in C major key, because there's no Bb "defined"; you will see it more likely in a song in key F major.
Dominant seventh chord
Some mentioned the "dominant seventh chord": the "dominant" is the 5th step of the scale; for C major, it is G. For F it is C, for G it is D. Together with the "sub-dominant", which is the fifth below the base tone, it forms the cadence: this is the sequence base chord (or tonic) - sub-dominant chord - dominant chord - base chord (tonic). For C major, it are the chords C - F - G - C, for F major, they are F - Bb - C - F. Play them and you'll notice that many songs use that scheme.
Now when you play C - F at the end, this sounds like a "real end", that's why this is called the "authentic end". If you play C7 - F, it sounds still more like that, but you still go from the dominant to the tonic. This is why the C7 chord is called the "dominant seventh chord" in that context.
(C7 - F sounds a little more beautiful than C - F, because it contains that tone Bb goes to tone A (the third tone of the F chord). This half tone step sounds lovley.)
Whereas a seventh chord virtually always "wants" to be "resolved" to the chord a fifth below, this needs not always be so. E.g. you may well use the chord sequence C7 - F7 - G7 - C7 to accopmany a song. Sounds cool.
The "above Bb" issue: inversions
Now to your last question, about starting the C7 from Bb. As i said, C7 consists of the tones C, E, G and Bb. Now, actually that's just the set of tones that may be used in the C7 chord. Now there's the concept of "chord inversion".
I explain it for the C chord first: it has tones C - E - G. In German we call that the "quint (=fifth) position", because the fifth tone above the C is "on top" of the chord.
First inversion: put the C one octave up --> tones E - G - C, "octave position".
Now the bass tone is the E, giving the so called "sixth chord". It's used as transition chord, the usual chord sequence is: C - C/E - F. The /E means "E in the bass, not the C".
Second inversion: put the E one octave up --> tones G - C - E, "third position".
Now the bass tone is G, giving the so called "quart-sixth chord". It's also used as a transition chord, the usual chord sequence is: C - C/G - G. The /G means (again) "G in the bass, not the C".
Doing inversion once more, i.e. putting the G one octave higher, we are back at the original sequence C - E - G (only one octave higher, but that's not of importance for that subject).
Inversions for C7
Now we can also do inversion with the C7 chord:
Base: C - E - G - B7
1st: E - G - B7 - C ("quint-sext-chord")
2nd: G - B7 - C - E ("third-quart-chord") (rather seldom used)
3rd: B7 - C - E - G ("second chord")
(the strange names in brackets stem from the "basso continuo" theory - do not worry about it, you would only need it for classic music: e.g. a chembalo accompaniment then very often only noted the bass tones and some numbers or symbols written above it, telling which chord to play above the given bass tone - everything else was free to the player's art)
Now i guess the 3rd inversion above is the one you are talking about when saying "above Bb". It's also used very often as transition chord; the usual sequence is: C - C/Bb - F(/A), to note here that the bass goes down a scale. You might want to add Fm/Ab - C/G - G to the sequence - very familiar i suppose (but hard to play on the guitar alone. In a band you would divide it up between guitar and bass).
But how to play that on a guitar? As i said above, you need to look how to arrange the fingers on the neck... For C/Bb, there's the following option:
do a barré on 1st fret, and do 2nd fret on D string and 3rd fret on G string. When strumming, omit both E strings. Now the tones Bb - E - Bb - C ring, making up a C/Bb. Although it's a little limited, and the Bb is doubled, it does the job. On a piano it were far easier - you just would go down 1 tone with the left hand.
Scales and intervals
There's no real need to learn scales or intervals before learning to play an instrument. But if you want to understand all the theory behind notes and scores, it's the very foundation! But i know a lot of (good!) musicians who can't even read notes and scores... Music lives from what you put into it as a performer, not from the theory :-D