used just by itself, the て form can connect clauses; in this case, the different between just ~て and ~てから would be like the difference between "I'll look it up and call you back" and "I'll look it up, then call you back." The meaning doesn't really change, but I don't think から was specifically dropped from this sentence.
In casual conversation, lots of stuff gets dropped. ~ている to ~てる is just one example of this. Just wait until people start dropping particles on you
Also, in your first post, did you mean to say いろいろ?