BJT Model, Thoery, Usage, etc;

K is basically the "buffer" correct? Basically, if it's 2, you're going to make it so that the maximum Ice is 1/2 β*Ibe? To ensure that the transistor remains in saturation? (close to or at 0 ohms resistance across it's CE junction).

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K - is a safety margin. As you know the BJT current gain β (Hfe in data sheet) is not constant but vary with collector current and temperature.
See figure 1 on page 3
http://www.fairchildsemi.com/ds/PN/PN2222A.pdf
So to ensure that the β variations don't affect our circuit we use K factor.

Also, I'm still having trouble understanding Ibe.
You said it's always Ib = (Vin - Vbe)/Rb, which makes sense, but to how do you know Vbe? I found that Vc actually affects Ib, can you explain this?

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We can use data sheet to find Vbe for a given current or if Vbe<<Vin_min we can assume without great error that Vbe = 0.7V.
And when the BJT work in saturation region you can forget about early effect.