How is 12-bar blues harmonically possible? Cmaj scale doesn't really have a C7 - F7 - G7. Is it done by borrowing chords from other modes? There seems to be a C7 in C mixolydian, F7 in C dorian and G7 in C ionian(major).
The key word is 'harmonically'. Blues does not follow all the harmonic rules. While it technically can be harmonically analyzed and it mostly follows the rules at the end of the day it is different because it is based on some non harmonic ideas, like the blues scale. I may have gotten you to think that all out of key chords and notes can be explained by modes which is technically true, but it is not always useful to look at it that way. All most all music can be broken down that way, but most musicians just play around and find something that sounds good.
The blues pattern is pretty much a I-IV-V chord progression, but instead of them all being just major chords they are dominant 7th chords. It works and it sounds fine. Harmonically it doesn't make much sense, but there is no rule in music saying it has to make harmonic sense.
Music theory is a very powerful tool, but especially recently it is more of a guideline. Theory gives a good backbone for basic understandings of what harmonically makes sense and can explain a lot about a song. The rules can be broken and tones can be taken from outside the key without having to make harmonic sense especially if they sound good.
There seems to be a general confusion here. Everything you can play or imagine is possible. Theory is a means to describe music, but music is by no way bound to any theory whatsoever.
Major scales are typically not a good way to describe (or play) Blues. Better suited are scales that are aptly named "blues scales" (see http://en.wikipedia.org/wiki/Blues_scale for example). In most cases it's a minor pentatonic with a flat 5 and sometimes a sharp 7 added.
But again rule #1 in Blues is: if it sounds good and if it expresses what you are trying to say (such as "my wife left me", "no more booze in the fridge", "I have to work so darn hard", "my dog just ate my savings" etc.), then it's correct.
If you want to get all pedantic about it, you can think of the I7 chord as being a tonic and ALSO being V7->IV. In other words, you're chaining extended dominant structures together, and when you do so, you create momentary "local" resolution tendencies, but become detached from the grand-scheme dominant resolution architecture.
In the blues, the I chord and the IV chord can and sometimes do become vague as to which one is actually the tonic root. This ambiguity becomes "solved" when the V7 struts out into the spotlight, cementing the I7 as being "more root" than the IV.
Dominant resolution can become pretty weird-wired up. Go look at a chart for "Giant Steps" to get an example of this!